AB and CD are two chords of a circle . If BA and DC are produced, then they intersect each other at the point P. Prove that `angle PCB= angle PAD`.

If two chords AB and CD of a circle with centre, O, when producd intersect each other at the point P, prove that angle AOC- angle BOD=2 angle BPC .

In the adjoining figure, O is the centre of a circle and AB is one of its diameters. The legth of the chrod CD is equal to the radius of the circle. When AC and BD are extended, they intersect each other at a point P. find the value of angle APB

If two chords AB and CD of a circle with centre O, when produce intersect each other at the point P, then prove angleAOC-angleBOD = 2angleBPC .

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

AB and CD are two diameters of a circle. Prove that ADBC is a rectangle

Two chords AB and CD of a circle with centre O intersect each other at the point P. prove that AOD+ angle BOC = 2 angle PBC . If angle BOC are supplementary to each other, then prove that the two chords are perpendicular to each other.

Two chords AB and CD of the circle with centre at O intersect each other at an internal point P of the centre. Prove that angle AOD+ angle BOC=2 angle BPC

Two tangents drawn at the point A and B on a circle intersect each other at the point P. If angle APB=60^(@), then anglePAB=

In figure, bar(AB) is a diameter of the circle, bar(CD) is a chord equal to the radius of the circle. bar(AC) and bar(BD) when extended intersect at a point E. Prove that angle AEB = 60^@ .

ABC is an acute-angled triangle .AP is the diameter of the circumcircle of the triangle ABC, EB and CF are perpendiculars on AC and AB respectiely and they intersect each other at the point other at the point Q. Prove that BPCQ is a parallelogram.