AB and CD are two parallel chords of a cricle and AD and BC intersects each other at a point O inside the circle. Prove that AO=BO

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

Two chords AB and CD of a circle intersect at a internal point P of the circle. Prove that APxxBP=CPxxDP .

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

The two chords PQ and RS of a circle intersects each other at the point X within the circle. By joining P,S and R,Q prove that DeltaPXS and DeltaRSQ are similar. From this also prove that PX: XQ=RX : XS .

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

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

In trapezium ABCD , AB and DC are parallel. A straight line parallel to AB intersects AD and BC at the points E and F respectively. Prove that DE:EA=CF:FB .

Two radii OA and OB of a circle with centre O are perpendicular to each other. If two tangents are drawn at the point A and B intersect each other at the point T, prove that AB= OT and they bisect each other at a ridght angle.

AB is a diameter and AC is a chord of the circle with centre at Q. the radius parallel to AC intersect the circle at D. Prove that D is the mid-point of the are BC.

QR is a chord of the circle with centre O. Two tangents drawn at eh points Q and R intersect each other at the point P. If QM is a diameter, prove that angle QPR=2 angleRQM[GP-X]