Question

if the angle between two tangents from an external point P to a circle of radius a and centre O, is 60°, then find the length of OP

Answer 1

Let the normal (point of contact) be Q and R respectively

Join OP then angle will be 30°

Then in tri.PQO

Tan 30°=OQ/PQ

$1 \div \sqrt{3} = a \div pq$

$pq = a \div \sqrt{3}$