Question

To draw a pair of tangents to a circle which are inclined to each other at an angle of 50°,it is required to draw tangents at end points of the two radii of the circle, such that the angle between the two radii should be :

Answer 1

Step-by-step explanation:

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=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 90o

. ∴ 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

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