**DATE OF SUBMISSION-4/1/2011**

Q.1- E, F, G, H are respectively the mid points of the sides of a parallelogram ABCD . show that

2ar (EFGH)=ar(ABCD)

Q.2- The diagonals of a parallelogram ABCD intersect at O. a line through O meets AB at P and CD at, show that ar(APQD)=1/2ar(parallelogramABCD).

Q.3-P is the point in the interior of the parallelogram ABCD , show that ar(APB)+ar(CPD)=ar(APD)+ar(BPC)

Q.4- ABCD is a quadrilateral and BE parallel AC and BE meets DC produced at E. show that ar(triangle DE)=ar(quad.ABCD).

Q.5-ABCD is a trapezium .ABparallel DC.A line parallel to AC intersects AB at X and BC at Y. prove that ar (triangleADX)=ar(triangleACY).

Q.6-Distance of a chord AB of a circle from the centre is 12cm and length of a chord is 10cm. Find the diameter of the circle.

Q.7-PQ and RS are two parallel chords of a circle on the same side of centre O and radius is 10cm. if PQ=16cm and RS =12cm.find distance between the chords.

Q.8- A line L intersects two concentric circles at A ,B,C and D .Prove that AB=CD.