ABCD is a cyclic quadrilaterla. Extended AB and DC intersect at P. Prove that PA.PB = PC.PD.

PQRS is cyclic quadrilateral. Extended PQ and SR intersect each other at A . Prove that AP.AQ=AR.AS .

ABCD is a cyclic quadrilateral. If AB = DC, then prove that AC= BD.

AB and CD are two chords of a cricle. Extended BA and CD intersect at P. Prove that anglePCB = anglePAD .

ABCD is a cyclic quadrilateral. The side BC of it is extended to E . Prove that the two bisectors of angleBADandangleDCE meet on the circumferncee of the circle .

ABCD is a cyclic quadrilateral. The bisectors of angleDAB and angleBCD intersect the circle at the points X and Y respectively. Prove that XY is a diameter of the circle.

ABCD is a cyclic quadrilateral. AB and DC are produced to meet at P. If angleADC = 70^@ and angleDAB = 60^@ , then anglePBC + anglePCB is equals___

ABCD is a cyclic quadrilateral .The chord DE is the external bisector of angleBDC Prove that AE (or extended AE), is the external bisector of angleBAC .

ABCD is a cyclic quadrilateral. The two sides AB and CD are produced to meet in the point P and other two sides AD and BC are produced to meet in the point R . The two circumcircle of DeltaBCPandDeltaCDR intersect at the point T . Prove that points P , T , R are collinear.

ABCD is a cyclic quarilateral. The bisectors of angleaandangleC in tersect the circle at the points E and F respectively . Prove that EF is a diameter of the circle.