Question

In the adjoining figure, XY and X'Y' are parallel tangents to a circle with centre O. Another tangent AB touches the circle at C intersecting XY at A and X'Y' at B. Prove that AB subtends right angle at the centre of the circle; or ∠AOB = 90°.

Assertion (A) : Tangents drawn at the end points of a diameter of a circle are always parallel to each other. Reason (R) : The lengths of tangents drawn to a circle from a point outside the circle are always equal.

Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

If tangents PA and PB drawn from an external point P to the circle with centre O are inclined to each other at an angle of 80° as shown in the given figure, then the measure of ∠POA is :