Question

From a point T outside a circle of centre O, tangents TP and TQ are drawn to the circle. Prove that OT is the right bisector of line segment PQ.

Answer 1

Given : A circle with centre O. Tangents TP and TQ are drawn from a point T outside a circle.

To Prove : OT is the right bisector of line segment PQ. 

Construction : Join OP & OQ 

Proof : In ∆PTR and ∆QTR 

In ∆OPT and ∆OQT 

∠OPT = ∠OQT = 90° 

OP = OQ (radius) 

OT = OT (Common) 

∆OPT ≅ ∆OQT(By RHS congruence) 

∠PTR = ∠QTR (cpct)

Therefore TR or OT is the right bisector of line segment PQ.