Question

A pair of tangents to a circle which is inclined to each other at an angle of 60° are drawn at ends of two radii. The angle between these radii must be:

Answer 1

Answer:

$\huge\blue {\underline \red{\fbox{required \: answer}}}$

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°

To find out-

• ∠ROQ=?

Solution-

• ∠OQP=90°

=∠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°

. ∴ By angle sum property of quadrilaterals, we get

• ∠OQP+∠RPQ+∠ORP+∠ROQ=360°

⟹90° +60°+90°+∠ROQ=360°

⟹∠ROQ=120°

Answer 2

Answer:

120

Step-by-step explanation:

90+90+60+x=360

then

240+x=360

x=360-240

x=120