Question

Two parallel tangents of a circle meet a third tangent at points P and Q. prove that PQ subtends a right angle at the centre.

Answer 1

Join OP, OQ, OA, OB and OC.

In ΔOAP and ΔOCP

OA = OC (Radii of the same circle)

OP = OP (Common)

PA = PC (Tangents from P)

∴ By side – side – side criterion of congruence,

ΔOAP ≅ ΔOCP ( SSS postulate)

The corresponding parts of the congruent triangles are congruent.