Question

A circle is touching the side bc of triangle abc

Answer 1

Lengths of tangents drawn from an external point to a circle are equal.

⇒ AQ = AR, BQ = BP, CP = CR.

Perimeter of ΔABC = AB + BC + CA = AB + (BP + PC) + (AR – CR) = (AB + BQ) + (PC) + (AQ – PC) [AQ = AR, BQ = BP, CP = CR] =AQ + AQ = 2AQ ⇒ AQ = 1/2 (Perimeter of ΔABC) ∴ AQ is the half of the perimeter of ΔABC.