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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.
Solution
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
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