Question

Prove that the angle between two tangent drawn from external point is supplementary to the angle sub tended by the line segment joining the point of contact at the centre

Answer 1

Here is your answer.

Answer 2

Given:
A circle with Centre O.AP and B P are tangents to the circle.

To prove :
<AOB+<APB=180°

Proof:
<OAP=90°
<OBP=90°
{ radius is perpendicular to the tangent}

In quadrilateral AOBP by angle sum property,
<OAP +<OBP +<AOB +<APB=360°
90°+90° +<AOB+<APB=360°
Therefore,
<AOB +<APB=360°-180°
=180°.