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.

PA and PB are tangents drawn from the external point P to the circle with centre O. In quad. OAPB, \[\begin{aligned} & \angle \mathrm{OAP}+\angle \mathrm{APB}+\angle \mathrm{OBP}+\angle \mathrm{AOB}=360^{\circ} \\ & 90^{\circ}+\angle \mathrm{APB}+90^{\circ}+\angle \mathrm{AOB}=360^{\circ}(\text { Tangent } \perp \text { radius }) \\ & \angle \mathrm{APB}+\angle \mathrm{AOB}=360^{\circ}-180^{\circ}=180^{\circ} \end{aligned} \]