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-segment joining the points of contact at the centre.

Answer 1

Draw a circle with center O and take a external point P. PA and PB are the tangents.

As radius of the circle is perpendicular to the tangent.

In Quadrilateral OAPB, sum of all interior angles = 360°

It proves the angle between the two tangents drawn from an external point to a circle supplementary to the angle subtented by the line segment