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

ABCD is trapezium with AB || DC. The diagonal AC and BD intersect at E . If Delta AED ~ Delta BEC . Prove that AD = BC .

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

In a quadrilateral ABCD, it is given that AB |\|CD and the diagonals AC and BD are perpendicular to each other. Show that AD.BC >= AB. CD .

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.

Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at the point ‘O’. Using the criterion of similarity for two triangles, show that (OA)/(OC) = (OB)/(OD) .

ABCD is a trapezium in which AB||DC and P,Q are points on AD and BC respectively, such that PQ||DC if PD=18 cm , BQ= 35 cm and QC= 15 cm, find AD.

Attempt any Two of the following: In squareABCD ,seg AB ||seg CD . Diagonal AC and BD intersect each other at point P . Prove : (A(DeltaABP))/(A(DeltaCPD))=(AB^(2))/(CD^(2))

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 .

In the adjoing figure, squareABCD is a square. DeltaBCE on side BC and DeltaACF on the diagonal AC are similar to each other. Then, show that A(DeltaBCE)=(1)/(2)A(DeltaACF)