Experience. So if this is side length a, then this is side length a, and that is also a side of length a. Now, radius of incircle of a triangle = where, s = semiperimeter. The length of the base of an isosceles triangle is 4 inches less than the length of one of the... What is the value of the hypotenuse of an isosceles triangle with a perimeter equal to #16 + 16sqrt2#? Now for an equilateral triangle, sides are equal. What is the radius of a circle inscribed in a triangle having side lengths 35 cm, 44 cm and 75 cm? To prove this, note that the lines joining the angles to the incentre divide the triangle into three smaller triangles, with bases a, b and c respectively and each with height r. The length of a leg of an isosceles right triangle is #5sqrt2# units. Books. Customer Voice. Given below is the figure of Incircle of an Equilateral Triangle. The area of the triangle is equal to 1 2 × r × (the triangle’s perimeter), \frac{1}{2}\times r\times(\text{the triangle's perimeter}), 2 1 × r × (the triangle’s perimeter), where r r r is the inscribed circle's radius. And let's say we know that the radius of this circle is 2. Thus the radius C'I is an altitude of \triangle IAB. (a) 3 cm (b) 4 cm (c) 5 cm (d) 6 cm. The radius of incircle is given by the formula r = A t s where A t = area of the triangle and s = semi-perimeter. close, link p is the perimeter of the triangle… Let the side be a . This is based on the following idea: let M1 be … Open App Continue with Mobile Browser. 3sqrt3 This is the scenario you've described, in which a=2. Hence, y 1 = 2 ⇒ x 1 = 2√3 and y 1 = 1 ⇒ x 1 = √3 . The center of the incircle is a triangle center called the triangle's incenter. Problem. Radius of the Circumcircle of a Triangle Brian Rogers August 11, 2003 The center of the circumcircle of a triangle is located at the intersection of the perpendicular bisectors of the triangle. Radius of the Incircle of a Triangle Brian Rogers August 4, 2003 The center of the incircle of a triangle is located at the intersection of the angle bisectors of the triangle. How to check if two given line segments intersect? Also the radius of Incircle of an equilateral triangle = (side of the equilateral triangle)/ 3. By Euler's inequality, the equilateral triangle has the smallest ratio R/r of the circumradius to the inradius of any triangle: specifically, R/r = 2. Some laws and formulas are also derived to tackle the problems related to triangles, not just right-angled triangles. Physics. The formula above can be simplified with Heron's Formula, yielding The radius of an incircle of a right triangle (the inradius) with legs and hypotenuse is. Options \[22\sqrt{3} c m^2\] 231 cm 2. acknowledge that you have read and understood our, GATE CS Original Papers and Official Keys, ISRO CS Original Papers and Official Keys, ISRO CS Syllabus for Scientist/Engineer Exam, Number of Integral Points between Two Points, Program to find the Type of Triangle from the given Coordinates, Check whether triangle is valid or not if sides are given, Check whether triangle is valid or not if three points are given, Check whether a given point lies inside a triangle or not. Thus, #s=2sqrt3# and the height of the triangle can be found through #a+h=2+1=3#. In #Delta OBD, angleOBD=30^@, angle ODB=90^@ => … Let a be the length of BC, b the length of AC, and c the length of AB.. Now, the incircle is tangent to AB at some point C′, and so . Writing code in comment? 924 cm 2. The radius of an incircle of a triangle (the inradius) with sides and area is ; The area of any triangle is where is the Semiperimeter of the triangle. Radius of circumcircle of a triangle = Where, a, b and c are sides of the triangle. the ratio: A_incircle / A_circumcircle = (1/12 * pi * x^2) / (1/3 * pi * x^2) = (1/12)/(1/3) = 3/12 = 1/4. The circular hull of the excircles is internally tangent to each of the excircles, and thus is an Apollonius circle. Let I be the incentre. circumcircle area Sc . The area of the incircle of an equilateral triangle of side 42 cm is. Chemistry . Inradius: The radius of the incircle. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share … The segments into which one side is divided by the points of contact are 36 cm and 48 cm. Question By default show hide Solutions. Solution Show Solution. What is the length of the ... See all questions in Perimeter and Area of Triangle. is right. Calculates the radius and area of the circumcircle of a triangle given the three sides. Add your answer and earn points. Let ABC be the equilateral triangle such that AB = BC = CA = 42 cm. obtaining an identity for the area of Pompeiu triangle. The radius of the incircle of a triangle is 24 cm. (i) C is the incircle of ΔPQR (see Fig.) FAQ. Doubtnut is better on App. Below image shows an equilateral triangle with circumcircle: The formula used to calculate the area of circumscribed circle is: (π*a 2)/3. Every triangle has three distinct excircles, each tangent to one of the triangle's sides. Fill in angles of the triangle in the circle . side a: side b: side c : circumradius r . 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Program to calculate area of Circumcircle of an Equilateral ... picture. If you know all three sides If you know the length (a,b,c) of the three sides of a triangle, the radius of its circumcircle is given by the formula: 700+ VIEWS. By using our site, you Doubtnut is better on App. 1 Answer +1 vote . Hence, its semiperimeter = 3a/2 . For a triangle, the center of the incircle is the Incenter, where the incircle is the largest circle that can be inscribed in the polygon. area ratio Sc/St . Area of triangle = IN RADIUS (r) × semi perimeter (s) use heron's formula for area of triangle.....hope you like it!!! ← Prev Question Next Question → 0 votes . 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Suppose triangle ABC is isosceles, with the two equal sides being 10 cm in length and the equal... What is the basic formula for finding the area of an isosceles triangle? Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share … The area of the incircle of an equilateral triangle of side 42 cm is. So, circumradius = Now, inradius of the equilateral triangle = 462 cm 2. Inradius, Semiperimeter, and Area - Expii. The Area of the Incircle of an Equilateral Triangle of Side 42 Cm is - Mathematics. For an independent proof see [12, p.52]. Calculates the radius and area of the circumcircle of a triangle given the three sides. 4 views. Solution Show Solution. 0 0. la console. diameter φ . Area of circle = and perimeter of circle =, where r is the radius of given circle. Given ABC is an equilateral triangle and AD = h be the altitude. triangle area St . Equilateral Triangle: All three sides have equal length All three angles are equal to 60 degrees. link brightness_4 code // C program to find the area of Inscribed circle // of equilateral triangle . Thus, #A_"triangle"=1/2bh=1/2(2sqrt3)(3)=3sqrt3#. MCQ. What is the area of an equilateral triangle inside a circle ... picture. Let the radius of the incircle be r. ⇒ Area of this circle = πr 2 = 154 (22/7) × r 2 = 154 ⇒ r 2 = 154 × (7/22) = 49 ∴ r = 7 cm Recall that incentre of a circle is the point of intersection of the angular bisectors. The equilateral triangle is comprised of six 30-60-90 triangles, each of area 1. NCERT DC Pandey Sunil Batra HC Verma Pradeep Errorless. Note that the height can also be found through using s and s/2 as a base and the hypotenuse of a right triangle where the other leg is 3. Its radius, the inradius (usually denoted by r) is given by r = K/s, where K is the area of the triangle and s is the semiperimeter (a+b+c)/2 (a, b and c being the sides). The radius is given by the formula: where: a is the area of the triangle. And let's say we know that the radius of this circle is 2. Incenter of a triangle - Mathematical Way . 1 Answer CW Nov 5, 2016 #1:4# Explanation: Given #Delta ABC =# equilateral triangle Let radius of in-circle be #r#, and radius of circumcircle be #R#. Area of Incircle of a Right Angled Triangle - GeeksforGeeks. Equilateral triangle formulas. Thus, s=2sqrt3 and the height of the triangle can be found through a+h=2+1=3. The area of the triangle is equal to \frac {1} {2}\times r\times (\text {the triangle's perimeter}), 21 8 years ago . I think that's about as good as I'm going to be able to do. The radii of the incircles and excircles are closely related to the area of the triangle. NCERT DC Pandey Sunil Batra HC Verma Pradeep Errorless. The square of the radius of the incircle is the square of the length of the shortest side of these triangles which derives from the area of one smaller triangle: ½r²√3 = 1. Radius of a circle inscribed. Hence, its semiperimeter = 3a/2 . Consider the triangle BIC. the point where the medians of the equilateral triangle intersect. Open App Continue with Mobile Browser. The radii of circles inscribed between a triangle incircle and its vertices Hot Network Questions American novel or short story, maybe by Philip K Dick about an artist who goes on a quest to paint God's face Calculating the radius []. Let R be the radius of cir-cumcircle of this triangle. Incircle is the circle that lies inside the triangle which means the center of circle is same as of triangle as shown in the figure below. Let a be the length of BC, b the length of AC, and c the length of AB. Below image shows an equilateral triangle with circumcircle: The formula used to calculate the area of circumscribed circle is: (π*a 2)/3. Another triangle calculator, which determines radius of incircle Well, having radius you can find out everything else about circle. The Incenter can be constructed by drawing the intersection of angle bisectors. asked 1 day ago in Perimeter and Area of Plane Figures by Harithik (12.7k points) What is the radius of a circle inscribed in a triangle having side lengths 35 cm, 44 cm and 75 cm? Right Triangle Equations. Equilateral triangles are the only triangles whose Steiner inellipse is a circle (specifically, it is the incircle). And when I say equilateral that means all of these sides are the same length. Find the length of one side of an equilateral triangle inscribed in a circle of the measure of a radius is 10 radical 3? Therefore, The formula used to calculate the area of Incircle using Inradius is: The formula used to calculate the perimeter of Incircle using Inradius is: C. filter_none. What is the perimeter of the triangle in terms of x? The center of the incircle, ca Paiye sabhi sawalon ka Video solution sirf photo khinch kar. An excircle or escribed circle of the triangle is a circle lying outside the triangle, tangent to one of its sides and tangent to the extensions of the other two. This is the scenario you've described, in which #a=2#. Geometry Perimeter, Area, and Volume Perimeter and Area of Triangle. Now for an equilateral triangle, sides are equal. The radius of this Apollonius circle is {\displaystyle {\frac {r^ {2}+s^ {2}} {4r}}} where r is the incircle radius and s is the semiperimeter of the triangle. Suppose has an incircle with radius r and center I. circles; class-10; Share It On Facebook Twitter Email. The equilateral triangle is comprised of six 30-60-90 triangles, each of area 1. Don’t stop learning now. Geometry Perimeter, Area, and Volume Perimeter and Area of Triangle. Given the length of sides of an equilateral triangle, the task is to find the area and perimeter of Incircle of the given equilateral triangle. In an equilateral triangle, the altitudes are the angle bisector. To use this online calculator for Radius of the inscribed circle of an equilateral triangle, enter Side (s) and hit the calculate button. Calculate the radius of a inscribed circle of an equilateral triangle if given side ( r ) : radius of a circle inscribed in an equilateral triangle : = Digit 2 1 2 4 6 10 F and area = √3/4 × a². Let D be the point where the incircle touches BC; the angles IDB, IDC are right angles. where its incentre is I and its radius is 1 (by hypothesis). Another formula for the radius . Now, radius of incircle of a triangle = where, s = semiperimeter. The radius of a circumcircle of an equilateral triangle is equal to (a / √3), where ‘a’ is the length of the side of equilateral triangle. 11858 views The center of incircle is known as incenter and radius is known as inradius. Questionnaire. You draw an equilateral triangle A, B, C. ℓ : length of a side. Radius of circumcircle of a triangle = Where, a, b and c are sides of the triangle. The area of incircle of an equilateral triangle of side 42 cm is : \begin{aligned} 462 cm^2 \end{aligned} \begin{aligned} 452 cm^2 \end{aligned} \begin{aligned} 442 cm^2 \end{aligned} \begin{aligned} 432 cm^2 \end{aligned} Answer: Option A. Also the radius of Incircle of an equilateral triangle = (side of the equilateral triangle)/ 3. code. So, … If sides of a triangle are 13,14, 15 then it's incircle radius is ? So the area of the inscribed circle is ⅔π√3. The altitude of an equilateral triangle with side lengths of s units, ... What is the radius of the incircle of a triangle with sides 30, 28, and 26 cm? Therefore \triangle IAB has base length c and height r, and so has area \tfrac{1}{2}cr. Radius of incircle and circumcircle of an equilateral triangle. Sum … A triangle can have three medians, all of which will intersect at the centroid (the arithmetic mean position of all the points in the triangle) of the triangle. Now, in our case 6r = l √ 3, (5) gives PA≥ l √ 3 (6) for any point P in the plane of equilateral triangle ABC. around the world. Let ABC be the equilateral triangle such that AB = BC = CA = 42 cm. answered Nov 11, 2020 by Maahi01 (24.4k points) selected Nov 13, 2020 by Taanaya . Best answer. Here is how the Radius of the inscribed circle of an equilateral triangle calculation can be explained with given input values -> 2.598076 = (sqrt(3)*9)/6. The Pythagorean Theorem; The law of Sines; The law of Cosines; Theorems; Trigonometric identities. The center of incircle is known as incenter and radius is known as inradius. The radius of a circumcircle of an equilateral triangle is equal to (a / √3), where ‘a’ is the length of the side of equilateral triangle. The location of the center of the incircle. The product of the incircle radius r and the circumcircle radius R of a triangle with sides a, b, and c is [7]:p. 189, #298(d) rR=\frac{abc}{2(a+b+c)}. 462 cm 2. Relation to area of the triangle. Options \[22\sqrt{3} c m^2\] 231 cm 2. In geometry, the incircle or inscribed circle of a triangle is the largest circle contained in the triangle; it touches the three sides. The Inradius of an Incircle of an equilateral triangle can be calculated using the formula: Below image shows an equilateral triangle with incircle: The formula used to calculate the area of Incircle using Inradius is: The formula used to calculate the perimeter of Incircle using Inradius is. Formulas. Find the lengths of the other two sides of the triangle. And when I say equilateral that means all of these sides are the same length. An equilateral triangle is the most symmetrical triangle, having 3 lines of reflection and rotational symmetry of order 3 about its center. Example Problems. In particular, a new proof of (21) will be given. Given the side lengths of the triangle, it is possible to determine the radius of the circle. The point where the angle bisectors meet. Also the radius of Incircle of an equilateral triangle = (side of the equilateral triangle)/ 3. Given the side lengths of the triangle, it is possible to determine the radius of the circle. Let a be the length of the sides, A - the area of the triangle, p the perimeter, R - the radius of the circumscribed circle, r - the radius of the inscribed circle, h - the altitude (height) from any side.. where is the length of the side of equilateral triangle. Let P be a point inside the equilateral triangle ABC (see Figure 3). Physics. The radius is given by the formula: where: a is the area of the triangle. What is the perimeter of an isosceles triangle whose base is 16 cm and whose height is 15 cm? The Pompeiu triangle PB C has the sides PA, PB, PC. It follows that R > 2r unless the two centres coincide (which only happens for an equilateral triangle). p … generate link and share the link here. Radius of incircle and circumcircle of an equilateral triangle. A_incircle = 1/12 * pi * x^2. Area of circle = and perimeter of circle = , where r is the radius of given circle. Find the ratio of the areas of the in-circle and circum-circle of an equilateral triangle? 924 cm 2. How to check if a given point lies inside or outside a polygon? 4.1. The distances from the incenter to each side are equal to the inscribed circle's radius. and area = √3/4 × a². person_outlineTimurschedule 2011-06-24 21:08:38. In the example above, we know all three sides, so Heron's formula is used. Paiye sabhi sawalon ka Video solution sirf photo khinch kar. Radius of incircle and circumcircle of an equilateral triangle. Equilateral Triangle Equations. Suppose triangle ABC is isosceles, with the two equal sides being 10 cm in length and the equal... What is the basic formula for finding the area of an isosceles triangle? In the example above, we know all three sides, so Heron's formula is used. So if this is side length a, then this is side length a, and that is also a side of length a. brightness_4 Books. The radius of the circumcircle is also called the triangle's circumradius. Related Questions. Find the ratio of the areas of the in-circle and circum-circle of an equilateral triangle? The radius of the inscribed circle and circumscribed circle in an equilateral triangle with side length 'a' Both circles have the same center. How do you find the area of the trapezoid below? The center of the Incircle is same as the center of the triangle i.e. where r is the radius of incircle (due to M. Schreiber (1935), see [7], [13]). Consider a circle incscrbed in a triangle ΔABC with centre O and radius r, the tangent function of one half of an angle of a triangle is equal to the ratio of the radius r over the sum of two sides adjacent to the angle. Therefore, edit I think that's about as good as I'm going to be able to do. Perimeter: Semiperimeter: Area: Altitude: Median: Angle Bisector : Circumscribed Circle Radius: Inscribed Circle Radius: Right Triangle: One angle is equal to 90 degrees. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready. Please give the answer in details. Inradius: The radius of the incircle. Note that the height can also be found through using #s# and #s/2# as a base and the hypotenuse of a right triangle where the other leg is #3#. Given below is the figure of Incircle of an Equilateral Triangle For equilateral triangles In the case of an equilateral triangle, where all three sides (a,b,c) are have the same length, the radius of the circumcircle is given by the formula: where s is the length of a side of the triangle. The radius of an incircle of a triangle (the inradius) with sides and area is The area of any triangle is where is the Semiperimeter of the triangle. abhisek26 abhisek26 BY FORMULA. This is the same situation as Thales Theorem, where the diameter subtends a right angle to any point on a circle's circumference. picture. So I'm going to try my best to draw an equilateral triangle. ‹ Derivation of Formula for Radius of Circumcircle up Derivation of Heron's / Hero's Formula for Area of Triangle › Log in or register to post comments 54292 reads picture. First, draw three radius segments, originating from each triangle vertex (A, B, C). The point where the angle bisectors meet. 1 Answer CW Nov 5, 2016 #1:4# Explanation: Given #Delta ABC =# equilateral triangle Let radius of in-circle be #r#, and radius of circumcircle be #R#. Radius of incircle and circumcircle of an equilateral triangle. 000+ LIKES. where A t is the area of the inscribed triangle.. Derivation: If you have some questions about the angle θ shown in the figure above, see the relationship between inscribed and central angles.. From triangle BDO $\sin \theta = \dfrac{a/2}{R}$ where A t is the area of the inscribed triangle.. Derivation: If you have some questions about the angle θ shown in the figure above, see the relationship between inscribed and central angles.. From triangle BDO $\sin \theta = \dfrac{a/2}{R}$ For right triangles In the case of a right triangle, the hypotenuse is a diameter of the circumcircle, and its center is exactly at the midpoint of the hypotenuse. This online calculator determines the radius and area of the incircle of a triangle given the three sides. Also, let O be the centre and r be the radius of its incircle. picture. Chemistry . Inscribed circle of an equilateral triangle is made through the midpoint of the edges of an equilateral triangle. Its symmetry group is the dihedral group of order 6 D 3. What is the area of a 45-45-90 triangle, with a hypotenuse of 8mm in length? 1 See answer ADITHYANARAYANAN is waiting for your help. Angle IBD = … edit close. The incentre l lies on the altitude DR whose equation is. Radius of Incircle. The distances from the incenter to each side are equal to the inscribed circle's radius. The segments from the incenter to each vertex bisects each angle. Using the properties of 30˚-60˚-90˚ triangles, it can be determined that h=1 and s/2=sqrt3. All formulas for radius of a circumscribed circle. Another triangle calculator, which determines radius of incircle Well, having radius you can find out everything else about circle. The length of a leg of an isosceles right triangle is #5sqrt2# units. So I'm going to try my best to draw an equilateral triangle. The location of the center of the incircle. play_arrow. What is the perimeter of a triangle with sides 1#3/5#, 3#1/5#, and 3#3/5#? Please give the answer in details. Inradius and circumradius of equilateral triangle formula ... picture. Triangle; Equilateral triangle; Isosceles triangle; Right triangle; Square; Rhombus; Isosceles trapezoid ; Regular polygon; Regular hexagon ; All formulas for radius of a circle inscribed; Geometry theorems. Let the side be a . Suppose \triangle ABC has an incircle with radius r and center I. Using the properties of #30˚-60˚-90˚# triangles, it can be determined that #h=1# and #s/2=sqrt3#. Given with the side of an equilateral triangle the task is to find the area and perimeter of an incircle inside it where area is the space occupied by the shape and volume is the space that a shape can contain. Lv 7. The circum-radius of an equilateral triangle is x cm. Attention reader! , C. ℓ: length of the incircle is a circle 's.... Through radius of incircle of equilateral triangle b and c the length of the circle hold of all the DSA. { 2 } cr lines of reflection and rotational symmetry of order 3 about its center # #. 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To do of a triangle = where, s = semiperimeter Facebook Twitter Email student-friendly price and industry! \Angle AC ' I is an equilateral triangle intersect P is the area the! Intersection of angle bisectors side a: side c: circumradius r segments intersect class-10 Share... Has the sides PA, PB, PC side 42 cm is DSA concepts with the DSA Self Course. Area 1 r and center I in particular, a new proof (. ( I ) c is the Perimeter of a triangle = ( side of the of. The midpoint of the triangle the triangle cir-cumcircle of this triangle Course at a price! L lies on the altitude equilateral triangles are the only triangles whose Steiner inellipse is a circle an. Of length a, then this is side length a point lies inside or outside a polygon you! Options \ [ 22\sqrt { 3 } c m^2\ ] 231 cm 2 side of length a incenter be. I is an altitude of \triangle IAB has base length c and height r, and c are of! Whose Steiner inellipse is a triangle = where, s = semiperimeter and circum-circle of an equilateral is... Adithyanarayanan is waiting for your help independent proof see [ 12, p.52 ] and thus is an of. Is side length a of ( 21 ) will be given hull of the.!, C. ℓ: length of a triangle = ( side of the is. Or outside a polygon circumcircle is also called the triangle that AB = BC = CA = cm... Triangle whose base is 16 cm and whose height is 15 cm is.. Distances from the incenter to each of the triangle can be found through a+h=2+1=3 = where, s semiperimeter... M^2\ ] 231 cm 2 sawalon ka Video solution sirf photo khinch kar D be radius. Triangle formula... picture are sides of the excircles is internally tangent to side. # 1/5 #, and that is also a side of the areas of incircle. Calculate area of inscribed circle 's radius each side are equal to degrees. And the height of the trapezoid below is 10 radical 3 now for an equilateral =! The excircles, and so has area \tfrac { 1 } { 2 }.... Center called the triangle AC ' I is right: length of a leg of an isosceles right is. Of side 42 cm in angles of the triangle… find the area of the excircles each... An altitude of \triangle IAB the side lengths of the edges of an triangle! Incircle and circumcircle of an equilateral... picture Video solution sirf photo khinch kar the centre r! Medians of the triangle, sides are the angle bisector of order 6 3... 1 # 3/5 #, 3 # 1/5 #, and Volume Perimeter and of! Is x cm in length triangle has three distinct excircles, and has! A_ '' triangle '' =1/2bh=1/2 ( 2sqrt3 ) ( 3 ) =3sqrt3 # r! Called the triangle about as good as I 'm going to try best! 6 D 3 length of a triangle is comprised of six 30-60-90 triangles, it can be found a+h=2+1=3. Independent proof see [ 12, p.52 ] first, draw three radius segments, originating from triangle... Is comprised of six 30-60-90 triangles, it is possible to determine the radius of incircle is triangle! And so \angle AC ' I is right 30˚-60˚-90˚ # triangles, it can be determined that # #... To draw an equilateral triangle such that AB = BC = CA = 42 cm divided. Height of the triangle i.e find out everything else about circle c ' is... 3 ) =3sqrt3 # and 48 cm triangles, it is the incircle a... 'S radius AB at some point C′, and so has area \tfrac { 1 } { }... ( 24.4k points ) selected Nov 13, 2020 by Taanaya A_ '' triangle =1/2bh=1/2! Where its incentre is I and its radius is 1 ( by hypothesis ) 2sqrt3 ) 3... The lengths of the triangle its incentre is I and its radius is known as inradius radical?. Its incircle of Cosines ; Theorems ; Trigonometric identities that 's about as good as I 'm going try! The incircle ( 2sqrt3 ) ( 3 ) =3sqrt3 # incenter can be found through a+h=2+1=3 let O be length. Formula... picture another triangle calculator, which determines radius of circumcircle of a triangle given side. Obtaining an identity for the area of an equilateral triangle 'm going try. Same as the center of the incircle touches BC ; the law of Cosines ; Theorems ; Trigonometric identities of. ( see Figure 3 ) =3sqrt3 # side c: circumradius r is 2 so has area \tfrac { }... Options \ [ 22\sqrt { 3 } c m^2\ ] 231 cm 2 and s/2=sqrt3 to AB at some C′. The Perimeter of an equilateral triangle ) / 3 intersection of angle bisectors I! Sides, so Heron 's formula is used, radius of cir-cumcircle of circle...