ABCD is a trapezium in which AB||DC and its diagonals intersect each other at point ‘O’. Show that ` (AO)/(BO) = (CO)/(DO)` .

PQRS is a trapezium of which PS||QR . Its two diagonals PR and QS intersects each other at the point O . If PO=3 , RO=x-3 , SO=x-2 and OQ=3x-13 , then find the value of 'x'

In trapezium ABCD , BC||AD and AD=4cm . The two diagonals AC and BD intersect at the point O in such a way that (AO)/(OC)=(DO)/(OB)=(1)/(2) . Find the length of BC .

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, diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O. Prove that ar(DeltaAOD) = ar(Delta BOC).

In a trapezium ABCD, BC AD and AD = 4 cm. the two diagonals AC and BD intersect at the point O in such a way that AO/OC = DO/OB = 1/2. Calculate the length of BC.

Kamala have drawn a trapezium PQRS of which PQ||SR . If the diagonals PR and QS intersect each other at O , then prove that OP:OR=OQ:OS , If SR=2PQ , then prove that O is a point of trisection of both the diagonals.

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

ABCD is a parallelogram. The diagonals AC and BD intersect each other at ‘O’. Prove that ar(DeltaAOD) = ar(DeltaBOC) . (Hint: Congruent figures have equal area)

In the trapezium ABCD, AB || DC. The diagonals AC and BD of it intersects each other at O. Prove that DeltaAOD=DeltaBOC.

In an isosceles triangle ABC, with AB = AC, the bisectors of /_ B and /_ C intersect each other at O. Join A to O. Show that : (i) OB = OC (ii) AO bisects /_A