Question

To draw a pair of tangents to a circle which are inclined to each

other at an angle of 600

, it is required to draw tangents at end points

of those two radii of the circle , what should be the angle between

them​

Answer 1

Answer:

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=60 ^o.

To find out- ∠ROQ=?

Solution- ∠OQP=90 ^o

=∠ORP since the angle, between a tangent to a circle and the radius of the same circle passing through the point of contact, is 90 ^o

. ∴ By angle sum property of quadrilaterals, we get ∠OQP+∠RPQ+∠ORP+∠ROQ=360 ^o

⟹90 ^o

+60 ^o

+90^o

+∠ROQ=360^o

⟹∠ROQ=120 ^o