Question

In fig AP is a tangent to the circle with center O such that $OP=4cm$ and $\angle OPA={30}^{\circ }$, then AP=

• A. $2\sqrt{2}cm$
• B. $2cm$
• C. $2\sqrt{3}cm$
• D. $3-\sqrt{2}cm$

Answer 1

Answer: (C)

$2\sqrt{3}cm$

Given $OP=4cm,\angle OPA={30}^{\circ }$

As tangent will be perpendicular to radius of the circle

So $\angle OAP={90}^{\circ }$

In $△APO,\angle OAP={90}^{\circ }$

$⟹\cos \angle OPA=\frac{AP}{OP}$

$⟹\cos {30}^{\circ }=\frac{AP}{4}$

$⟹OA=4\times \frac{\sqrt{3}}{2}=2\sqrt{3}cm$