Question

In the given figure, $PAandPB$ are the tangents to a circle with center $O$. Show that the points $A,O,B,P$ are concyclic.

Answer 1

If the $4$ points are concyclic they lie on a circle.

Then the opposite angles of the quadrilateral formed are supplementary.

Here $\angle OAP=\angle OBP={90}^{\circ }$ (Angle made by tangent and normal)

$\therefore \angle OAP+\angle OBP={180}^{\circ }$(angle sum property of a quadrilateral)

Thus, $AOPB$ are concyclic.