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`.

In triangle ABC, AB gt AC and D is any point of BC. Prove that, AB gt AD.

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).

E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that DeltaABE ~ DeltaCFB .

In the given figure, two chords AB and CD of a circle intersect each other at the point P (when produced) outside the circle. Prove that DeltaPAC ~ DeltaPDB

In the given figure, two chords AB and CD of a circle intersect each other at the point P (when produced) outside the circle. Prove that PA*PB= PC*PD

In the given figure, two chords AB and CD intersect each other at the point P. Prove that AP*PB= CP*DP

In triangle ABC, the bisectors of angle B and angle C intersect at I. A line drawn through I and parallel to BC intersects AB at P and AC at Q. Prove that PQ = BP + CQ.

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

In the adjacent figure ABCD is a parallelogram P and Q are the midpoints of sides AB and DC respectively. Show that PBCQ is also a parallelogram.

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).