The diagonal AC of a parallelogram ABCD intersects DP at the point Q, where ‘P’ is any point on side AB. Prove that `CQ xx PQ = QA xx QD`.

A straight line drawn through D of the parallelogram ABCD intersects AB and the extended part of CB at the points E and F respectively. Prove that AD:AE=CF:CD .

The diagonals AC and BD of the parallelogram ABCD intersect each other at O . Any straight line passing through O intesects the sides AB and CD at the points P and Q respectively . Prove that OP = OQ.

The diagonals of a quadrilateral ABCD intersect each other at point ‘O’ such that (AO)/(BO) = (CO)/(DO) . Prove that ABCD is a trapezium

The bisectors of angleA and angleB of the parallelogram ABCD meet at the point P on the side CD. If the length of the side AB be 4 cm , find the length BC.

AC is a common diagonal to both the parallelograms ABCD and AECF. If the points B , E , D , F are not collinear , prove that BEDF is a parallelogram.

The centre of two circle are P and Q they intersect at the points A and B. The straight line parallel to the line segment PQ through the point A intersects the two circles at the point C and D Prove that CD = 2PQ

ABCD is a parallelogram. AC and BD are the diagonals intersect at O. P and Q are the points of tri section of the diagonal BD. Prove that CQ" ||" AP and also AC bisects PQ (see figure).

ABCD is a parallelogram. A circle passing through C and D intersects AD and BC at the points E and F. Prove that the four points E, A, B, F are concyclic.

DeltaABC and DeltaDBC are situated on the same base BC and on the same side of BC . E is any point on the side BC . Two line through the point E and parallel to AB and BD intersects the sides AC and DC at the points F and G respectively. Prove that AD||FG .