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

squareABCD is a parallelogram. A circle passing throught D, A, B cuts BC in P. Prove that DC=DP.

squareABCD is a parallelogram. Point E is on side BC , line DE intersects Ray AB in point . T Prove that : DExxBE=CExxTE .

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))

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 .

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 .

Prove that a line cannot intersect a circle at more two points .

Prove: In a parallelogram, opposite sides are equal.

ABCD is a parallelogram. L is a point on BC which divides BC in the ratio 1:2 . AL intersects BD at P.M is a point on DC which divides DC in the ratio 1 : 2 and AM intersects BD in Q. Point Q divides DB in the ratio

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

Two circles intersect at A and B. From a point P on one of the circles lines PAC and PBD are drawn intersecting the second circle at C and D. Prove that CD is parallel to the tangent at P.