Question

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

Answer 1

Since, tangents drawn from an external point are equally inclined to the line joining centre to that point.

Draw an image based on given instructions:

Here, PT is the tangent of the circle

OT ⊥ PT

And, ∠TPS = 60° (given)

∠TPO = 60°/2 = 30°

Now, from right ∆TPO:

sin 30° = OT/OP

1/2 = a/OP

or OP = 2a