CBSE Class 10 Maths (Standard) 2017 · Paper 30(B) · Question 25

Circles 4 marks Medium

A circle is touching the side

B C

of a

△ A B C

P

and touching the sides

A B

and

A C

when produced at

Q

and

R

respectively. Prove that

A Q = \frac{1}{2} (perimeter of △ A B C)

Answer

Since

2 A Q = A B + B C + C A

, we get

A Q = \frac{1}{2} (perimeter of △ A B C)

, as required.

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