Q. 23

Let us write by calculating the length of radius of incircle and circumcircle of a triangle of which sides are 20 cm, 15 cm, 25 cm. Let us calculate the area of the regions bounded by incricle and circum-circle.

Answer :

Let BCD is a triangle of sides BC, BD and DC equal to 20 cm, 15 cm, 25 cm. AB, AD and AC are the internal bisectors of respective angles of the triangle. The three internal bisectors meet at A. Perpendiculars drawn from A on sides BC, CD and DB are AG, AE and AF respectively.


AG = AE = AF


Legth of inner radius of triangle = AG



Let AG be r units.


The given triangle forms a right angled triangle with B = 90°



Using Pythagoras theorem,


BE2 +DE2 = BD2


BE2 + 12.52 = 152


BE2 = 68.75


BE = 8.3 cm


The centroid of triangle is at A and lies on height BE.



AE = 2.767 cm


r = 2.767 cm


Area of a circle = πr2



Area of incircle = 24 cm2



The given triangle forms a right angled triangle


BC will act as the diameter of the circumcircle centered at O.


Diameter = 25 cm


Radius = 12.5 cm


Area of a circle = πr2


Area of the circumcircle


Area of circumcircle = 491 cm2


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Surface Area of Right Circular CylinderSurface Area of Right Circular CylinderSurface Area of Right Circular Cylinder49 mins
Surface Area of Right Circular CylinderSurface Area of Right Circular CylinderSurface Area of Right Circular Cylinder52 mins
Surface Area and Volume of Right Circular ConeSurface Area and Volume of Right Circular ConeSurface Area and Volume of Right Circular Cone37 mins
Champ Quiz | Area of TriangleChamp Quiz | Area of TriangleChamp Quiz | Area of Triangle53 mins
Surface Area and Volume of Right Circular CylindersSurface Area and Volume of Right Circular CylindersSurface Area and Volume of Right Circular Cylinders42 mins
Champ Quiz | Area of ParallelogramChamp Quiz | Area of ParallelogramChamp Quiz | Area of Parallelogram55 mins
Quiz | Area and ParallelogramQuiz | Area and ParallelogramQuiz | Area and Parallelogram46 mins
Quiz | Area of Parallelogram and TrianglesQuiz | Area of Parallelogram and TrianglesQuiz | Area of Parallelogram and Triangles43 mins
NCERT |  Imp Qs on Area of Parallelogram And TrianglesNCERT |  Imp Qs on Area of Parallelogram And TrianglesNCERT | Imp Qs on Area of Parallelogram And Triangles44 mins
NCERT |  Imp. Qs. on Area of Parallelogram and TrianglesNCERT |  Imp. Qs. on Area of Parallelogram and TrianglesNCERT | Imp. Qs. on Area of Parallelogram and Triangles43 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :