The diagonals of a quadrilateral ABCD intersect each other at point ‘O’ such that `(AO)/(BO) = (CO)/(DO)`. Prove that ABCD is a trapezium

In the figure seg AC and seg BD intersects each other at point P and (AP)/(CP)=(BP)/(DP) . Then Prove that DeltaABP~DeltaCDP .

Diagonals of a trapezium ABCD with AB || DC, intersect each other at the point ‘O’. If AB = 2CD, find the ratio of areas of triangles AOB and COD.

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 .

If bisectors of angleA and angleB of a quadrilateral ABCD meet at O, then angleAOB is

In squareABCD, "seg " AD||"seg " BC. Diagonal AC and diagonal BC intersect each other in point P. Then show that (AP)/(PD)=(PC)/(BP)

Diagonal of a rectangle ABCD intersect at point P, angleBPC=50^@ . Then find anglePAD .

In the adjoining figure, two circles intersect each other at points A and E . Their common secant through E intersects the circle at points B and D . The tangents of the circles at point B and D intersect each other at point C . Prove that squareABCD is cyclic .

squareABCD is a trapezium in which AB|| DC and its diagonals intersect each other at points O . Show that AO : BO = CO : DO.