Question

If angle between two tangents drawn from a point P to a circle of radius a and centre O is 60°, then OP = `asqrt(3)`

Options

• True

• False

Answer 1

This statement is True.

Explanation:

From point P, two tangents are drawn

Given, OT = a

Also, line OP bisects the ∠RPT.

∴ ∠TPO = ∠RPO = 30°

Also, OT ⊥ PT

In right-angled ΔOTP,

`sin 30^circ = (OT)/(OP)`

⇒ `1/2 = a/(OP)`

⇒ OP = 2a