Question

In the given figure, PA is tangent to a circle with centre O. If ∠APO = 30° and OA = 2.5 cm, then OP is equal to:

Options

• 2.5 cm

• 5 cm

• `5/sqrt(3)` cm

• 2 cm

Answer 1

5 cm

Explanation:

Since PA is tangent to a circle at A.

∴ ∠OAP = 90°

∠APO = 30°   ...(Given)

sin (∠APO) = `(OA)/(OP)`

sin 30° = `2.5/(OP)`

sin 30° = `25/(10 xx OP)`

`1/2 = 5/(2 xx OP)`

⇒ OP = 5 cm