Question

Two tangents PA and PB are drawn from an external point P to a circle with centre O. Prove that AOBP is a cyclic quadrilateral.

Answer 1

Since, $OA\perp AP$ and $OB\perp BP$

$\angle PAO+\angle PBO={90}^o+{90}^o={180}^o$

$⟹\angle APB+\angle AOB={180}^o$

$⟹AOBPisacyclicquadrilateral$.