Prove that in two concentric circles, the chord of the larger circle, which touches the smaller circle, is bisected at the point of contact.

Question

TextTheorem on Tangent Perpendicular to Radius at Point of ContactConcentric CirclesPerpendicular from Centre Bisects the Chord

Assertion (A) : The tangents drawn at the end points of a diameter of a circle, are parallel. Reason (R) : Diameter of a circle is the longest chord.

In the given figure, AB is a diameter of the circle with centre O. AQ, BP and PQ are tangents to the circle. Prove that ∠POQ = 90°.