Question

From a point P, two tangents PA and PB are drawn to a circle with center O as shown. If ∠ AOB = 120°, then find the value of ∠ APB.

Answer 1

As a tangent is perpendicular to the radius through the point of contact,
$\angle PAO=\angle PBO={90}^{\circ }$

The sum of all angles in a quadrilateral is ${360}^{\circ }$.
$\angle APB={360}^{\circ }–\angle AOB–\angle PAO-\angle PBO$
$\Rightarrow \angle APB={360}^{\circ }–{120}^{\circ }–{90}^{\circ }-{90}^{\circ }$
$\Rightarrow \angle APB={60}^{\circ }$
Measure of ∠ APB is ${60}^{\circ }$.