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`.

Diagonal of a rectangle ABCD intersect at point P, angleBPC=50^@ . Then find anglePAD .

squareABCD is a parallelogram . Side BC intersects circle at point P . Prove that DC = DP .

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

squareABCD is a parallelogram. Point E is on side BC , line DE intersects Ray AB in point . T Prove that : DExxBE=CExxTE .

In the figure seg AC and seg BD intersects each other at point P and (AP)/(CP)=(BP)/(DP) . Then Prove that DeltaABP~DeltaCDP .

If a point Q lies between two points P and R such that PQ = QR, prove that PQ = 1/2 PR.

ABCD is parallelogram and ABEF is a rectangle and DG is perpendicular on AB. Prove that (i) ar (ABCD) = ar(ABEF) (ii) ar (ABCD) = AB xx DG

ABCD is a quadrilateral in which AB= AD, the bisector of angle BAC and angle CAD intersect the sides BC and CD at the points E and F respectively. Prove that EF || BD.

Draw three circles passing through the points P and Q, where PQ=4 cm

ABC is right - angled triangle at B. Let D and E be any two point on AB and BC respectively . Prove that AE^2 + CD^2 = AC^2 + DE^2