From an external point P, two tangents PA and PB are drawn to a circle with centre O. If angle APB = 70 degrees, find angle AOB.

Step 1: Identify properties of tangents and radii

A fundamental property of circles states that the radius drawn to the point of tangency is perpendicular to the tangent line. Therefore, the angle between radius OA and tangent PA is $90^\circ$, and the angle between radius OB and tangent PB is also $90^\circ$.

Step 2: Find $\angle$ AOB in quadrilateral OAPB

The sum of the interior angles in any quadrilateral is $360^\circ$. In quadrilateral OAPB, we know three angles: $\angle OAP = 90^\circ$, $\angle OBP = 90^\circ$, and the given $\angle APB = 70^\circ$. By subtracting the sum of these three angles from $360^\circ$, we can determine the measure of $\angle AOB$.

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