Question

If Δ PQR is isosceles with PQ = PR and a circle with centre O and radius r is the incircle of the  Δ PQR touching QR at T, prove that the point T bisects QR.

Answer 1

To proof:- QT = TR 

Proof: Let the circle touches sides PQ and PR at points A and B respectively. 

PA = PB , AQ = QT and BR = TR  .....(Lengths of tangents drawn from an external point to a circle are equal)

Given, PQ = PR 

PA + AQ = PB + BR 

AQ = BR        {Using (1)) 

⇒  QT = TR