In the given figure, PQ is a tangent at a point C to a circle with centre O. If AB is a diameter and ∠CAB = 30°. Find ∠PCA.

Question

TextTheorem on Tangent Perpendicular to Radius at Point of Contact

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°.