Question

Two tangents PA and PB are drawn to the circle with centre O, such that $\angle$APB =${120}^{\circ }$what is the relation between OP and AP?

• A. OP = 1/2 AP
• B. AP = 2 /3 OP
• C. OP = 2 AP
• D. OP = AP

Answer 1

The correct option is C

OP = 2 AP

$\angle$APB = ${120}^{\circ }$

$\angle$APO = ∠OPB=${60}^{\circ }$

cos ${60}^{\circ }$= $\frac{AP}{OP}$
$\frac{1}{2}$ = $\frac{AP}{OP}$

OP = 2AP