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`.

The diagonal BD of parallelogram ABCD intersect AE at F as shown in the figure. If E is any point on BC, then prove that DFxxEF=FB=FA .

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).

Throught the mid-point M of the sides of a parallelogram ABCD, the line BM is drawn intersecting AC at L, and AD produced to E. Prove that EL = 2 BL .

Diagonals AC and BD of a trapezium ABCD with AB |\| DC intersect each other at O. Prove that ar (AOD) = ar (BOC).

Diagonals AC and BD of a quadrilateral ABCD intersect each other at P. Show that ar (APB) xx ar (CPD) = ar (APD) xx ar (BPD). [Hint : From A and C, draw perpendiculars to BD.

In Fig. two chords AB and CD of a circle intersect each other at the point P (when produced) outside the circle. Prove that (i) Delta PAC ~ Delta PDB , (ii) PA . PB = PC . PD

In Fig . two chords AB and CD intersect each other at the point P. prove that : AP.PB=CP.DP

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

In Fig. 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