Question

If angle between two tangents drawn from a point P to a circle of radius a and centre O is 90°, then OP = ______.

Answer 1

If angle between two tangents drawn from a point P to a circle of radius a and centre O is 90°, then OP = `underlinebb(asqrt(2))`.

Explanation:

Let the tangents from P touch the circle at T and R. OT = a and OT ⟂ PT.

OP bisects the angle between the tangents, so each half is 45°. 

In right triangle OTP,

`sin 45^circ = (OT)/(OP) = a/(OP)` 

Hence `OP = a/(1/sqrt(2)) = asqrt(2)`.