ABCD is a parallelogram. Diagonals AC and BD interset at E. Show that the circumcircles of ` triangle ADE` and ` triangle BCE` touch at E

The sides AD, BC of a trapezium. ABCD are parallel and the diagonals AC and BD meet at O. If the area of triangle AOB is 3 cm and the area of triangle BDC is 8 cm2, then what is the area of triangle AOD?

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) .

ABCD is a parallelogram in which diagonals AC and BD intereset at O. If E, F, G and H are the mid points of AO, DO, CO and BO respectively, then the ratio of the perimeter of the quadrilateral EFGH to the perimeter of parallelogram ABCD is:

diagonal of a cocyclic parallelogram ABCD is AC and BD intersection at point R .then

ABCD is a parallelogram with AC and BD as diagonals. Then, A vec C - B vec D =

ABCD is a parallelogram, with AC, BD as diagonals. Then vec AC - vec BD =

ABCD is a parallelogram and [AC], [BD]are its diagonals. Express vec AC and vec BD in terms of vec AB and vec AD .

Let ABCD is a parallelogram and vec AC,vec BD be its diagonal,then vec AC+vec BD is

Diagonal AC of a parallelogram ABCD bisects A. Show that ABCD is a rhombus.