X, Y, Z and C are the points on the circumference of a circle with centre 'O'. AB is a tangent to the circle at 'X' and ZY = XY. Given ∠OBX = 32° and ∠AXZ = 66°. Find:

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TextTheorem on Tangent Perpendicular to Radius at Point of ContactAngle Subtended by Arc at Centre is Twice Angle at CircleAngles in Same Segment are EqualAlternate Segment Theorem for Tangent and Chord4 sub-questions

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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.

Assertion-ReasonDefinition of Tangent to a CircleTheorem on Tangent Perpendicular to Radius at Point of Contact

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°.

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