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

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

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 adjacent figure lines PQ and RS intersect each other at point O. If anglePOR : angleROQ = 5: 7, find all the angles.

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 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 adjoining figure, two circles intersect each other at points M and N . Secants drawn from points M and N intersect cirecls at point R, S, P and Q as shown in the figure.

In the adjoining figure "seg "Cebot" side " AB, " seg" AD bot" side " BC. Prove that (i) DeltaAEP~DeltaCDP (ii) DeltaAEP~DeltaADB

squareABCD is a parallelogram . Side BC intersects circle at point P . Prove that DC = DP .

Two circle with centre O and P intersect each other in point C and D. Chord AB of the circle with centre O touches the circle with circle with centre P in Point E. Prove that angleADE+angleBCE= 180^(@)

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 .