Question

In a circle of radius 5cm, angle between pair of tangents are twice of angle between the radii. Then angle between radii at the center is ___ ? A) 30 B) 60° C) 45° D) 90​

Answer 1

Answer:

Option C

Given- O is the centre of a circle to which a pair of tangents PQ&PR from a point P touch the circle at Q&R  respectively. ∠RPQ=60o.

To find out- ∠ROQ=?

Solution- ∠OQP=90o=∠ORP since the angle, between a tangent to  a circle and the radius of the same circle passing through  the point of contact, is 90o. ∴  By angle sum property of quadrilaterals, we get ∠OQP+∠RPQ+∠ORP+∠ROQ=360o⟹90o+60o+90o+∠ROQ=360o⟹∠ROQ=120o.

Ans- Option C.

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