ABCD is a rectangle. The line through C perpendicular to AC meets AB produced at X and AD produced at Y. Prove that the points D, B, X, Y are concyclic.

ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F. Show that: ar(AEDF) = ar(ABCDE)

ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F. Show that: ar(ACB) = ar(ACF)

ABCD is a parallelogram. A circle passing through C and D intersects AD and BC at the points E and F. Prove that the four points E, A, B, F are concyclic.

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 ( i )AR=2BC (ii) BR=2BQ.

In the adjoining figure, ABCD is a quadrilateral. A line through D, parallel to AC, meets BC produced in P . Prove that ar(triangleABP)=ar("qaud. ABCD") .

In the adjoining figure, ABCD is a parallelogram and E is the midpoint of AD. A line through D, drawn parallel to EB, meets AB produced at F and BC at L. Prove that (i) AF=2DC, (ii) DF=2DL

In figure, ABCDE is any pentagon. BP drawn parallel to AC meets DC produced at P and EQ drawn parallel to AD meets CD produced at Q. Prove that ar (ABCDE) = ar (DeltaAPQ) .

In figure, ABCDE is any pentagon. BP drawn parallel to AC meets DC produced at P and EQ drawn parallel to AD meets CD produced at Q. Prove that ar (ABCDE) = ar (DeltaAPQ) .

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.

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.