Two tangents `P Aa n dP B` are drawn from an external point `P` to a circle with centre `Odot` Prove that `A O B P` is a cyclic quadrilateral.

Two tangents PQ and PR are drawn from an external point to a circle with centre O . Prove that QORP is cyclic quadrilateral.

Two tangents PQ and PR are drawn from an external point to a circle with centre 0. Prove that QORP is cyclic quadrileral.

If the points of contact of the tangents drawn from an external points P to a circle with centre O be A and B,then show that PAOB is a cyclic quadrilateral.

Two tangents PA and PB are drawn from an external point P to a circle with centre at O. If AOB = 105^(@) the A hat(P) B is :

From a point P , two tangents P A and P B are drawn to a circle with centre O . If O P= diameter of the circle, show that /_\ A P B is equilateral.

AP and AQ are two tangents drawn from an external point A to a circle with centre O, P and Q are points of contact. If PR is a diameter, prove that OA||RQ.

Two tangents PA and PB are drawn to circle with centre O from an external point P. Prove that angleAPB= 2angleOAB

In Figure, P A and P B are tangents from an external point P to a circle with centre O . L N touches the circle at M . Prove that P L+L M=P N+M N .

Two tangents are drawn from an external point A of the circle with centre at O which touches the circle at the points B and C. Prove that AO is the perpendicular bisector of BC.