Question

Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segments joining the points of contact at the centre.

Answer 1

Given, PA and PB are the tangents drawn from a point P to a circle with center O. Also, the line segments OA and OB are drawn. 

To prove: ∠APB + ∠AOB = 180^o 

We know that the tangent to a circle is perpendicular to the radius through the point of contact.