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

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

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).

Through the mid point P of the side AD of a parallelogram ABCD, straight line BP is drawn cutting AC at R and CD produced at Q. Prove that bar(QR)=2bar(RB) .

ABCD is a parallelogram and P is themid point of the side AD. The line BP meets the diagonal AC in Q. Then the ratio AQ : QC =

In a parallelogram ABCD, P is the mid point of the side AD. The line BP cuts the diagonal AC in the point Q. Then the ratio AQ:QC=

In a rhombus ABCD the diagonals AC and BD intersect at the point (3, 4). If the point A is (1, 2) the diagonal BD has the equation

In the figure, diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O. Prove that ar(DeltaAOD) = ar(Delta BOC).

Diagonals of a trapezium ABCD with AB||DC . Intersect each other at the point 'O'. IF AB=2CD, find the ratio of areas of triangles AOB and COD.

Diagonals AC and BD of a trapezium ABCD with AB||DC intersect each other at the point 'O'.Using the criterion of similarity for two tri-angles , show that (OA)/(OC)=(OB)/(OD) .