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 $∠ A P B .$

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Solution

As a tangent is perpendicular to the radius through the point of contact,

$∠$ PAO = $∠$ PBO = $90^{\circ}$ .

The sum of all angles in a quadrilateral is $360^{\circ}$ .

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

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