Question

In the given figure, AP is a tangent to the circle with centre O such that OP = 4 cm and ∠OPA = 30°. Then,
AP =

(a) $2\sqrt{2}cm$

(b) 2 cm

(c) $2\sqrt{3}$ cm

(d) $3\sqrt{2}cm$

Answer 1

In the given figure,

if we join O and A, the line OA will be perpendicular to AP. This is because the radius of a circle will always be perpendicular to the tangent at the point of contact. Therefore, is a right triangle.

We know that,

…… (1)

We know that,

…… (2)

From equations (1) and (2), we have,

Therefore, option (c) is the correct answer.