Question

In the given figure, O is the center of a circle and two tangents CA, CB are drawn on the circle from a point C lying outside the circle. Prove that $\angle AOB$ and $\angle ACB$ are supplementary.

Answer 1

In MQNP,
$m\angle CAO={90}^0$ (Radius is perpendicular to the tangent)
$m\angle CBO={90}^0$ (Radius is perpendicular to the tangent)
$\therefore m\angle AOB+m\angle ACB={360}^0-m\angle CAO-m\angle CBO={360}^0-{90}^0-{90}^0={180}^0$
Hence, angle AOB and angle ACB are supplementary.