CBSE Class 10 Maths (Basic) 2025 · Paper 430(B)/S · Question 29(a)

Circles 3 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

produced at

Q

and

R

respectively. Prove that

A Q = \frac{1}{2} [perimeter of △ A B C]

Answer

Since

A Q = A R

and

A Q + A R = A B + B C + C A

, we get

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

, so

A Q = \frac{1}{2} [perimeter of △ A B C]

. Hence proved.

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