ABCD is a parallelogram. The circle through A, B and C intersect CD (produced if necessary) at E. Prove that AE = AD.

ABCD is a parallelogram. The circle through A,B is so drawn that it intersects AD at P and CB at Q. Prove that P,Q,C and D are concyclic.

ABCD is a parallelogram and a line through A meets DC at P and BC (produced) at Q. Prove that ar(triangleBPC) = ar(triangleDPQ)

ABCD is a parallelogram whose diagonals intersect at E. AC is produced to F such that CF = AE Prove that ar (DeltaBDF) = ar (|| gm ABCD) .

P is the mid point of side AB of a parallelogram ABCD. A line through B parallel to PD meets DC at Q and AD produced at R. prove that AR=2BC.

In Fig. . ABCD is a parallelogram and E is the mid-point of side BC. If DE and AB, when produced meet at F, prove that AF = 2AB.

In Fig. . ABCD is a parallelogram and E is the mid-point of side BC. If DE and AB, when produced meet at F, prove that AF = 2AB.

P is the mid point of side AB of a parallelogram ABCD. A line through B parallel to PD meets DC at Q and AD produced at R. prove that BR=2BQ.

ABCD is a parallelogram E is the mid point of AB and CE bisects angleBCD . Prove that: AE=AD?

ABCD is a cyclic quadrilateral. A circle passing through A and B meets AD and BC in E and F respectively. Prove that EF||DC

Two equal chords AB and CD of a circle C(O,r) when produced meet at a point E. Prove that: AE = CE