Question

From a point P, two tangents PA and PB are drawn to a circle with center O as shown.
If angle AOB = ${100}^{\circ }$, then find the value of $\angle APB.$

• A. ${40}^{\circ }$
• B. ${60}^{\circ }$
• C. ${80}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is C

${80}^{\circ }$

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 ${360}^{\circ }$.

So, $\angle$APB = ${360}^{\circ }$ – ${100}^{\circ }$ - ${90}^{\circ }$- ${90}^{\circ }$ = ${80}^{\circ }$.