ABCD is a parallelogram whose diagonals AC and BD intersect at O. A line through O intersects AB at P and DC at Q. Prove that ar `(Delta POA) =" ar "(Delta QOC)`.

If ABCD is a quadrilateral whose diagonals AC and BD intersect at O, then

The diagonals of a parallelogram ABCD intersect at O.A line through O intersects AB at X and DC at Y. Prove that OX=OY

ABCD is a trapezium with AB||DC. A line parallel to AC intersects AB at X and BC at Y. Prove that ar( Delta ADX) = ar( Delta ACY).

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

The diagonals of a parallelogram ABCD intersect at O. A line through O meets AB in x and CD in Y .Show that ar (AXYX)=(1)/(2)(ar|^(gm)ABCD)

Diagonal PR and QS of quadrilateral PQRS intersects at T such that PT= TR and PS= QR, show that ar (Delta PTS) =" ar "(Delta RTQ)

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.