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1.in a trapezium pqrs a and b are mid points of diagonals pr and qs show that ab=1/2(pqrs]

2.in the fig o is the center of circle and OLM is perpendicular to AOB prove that a] A, Q, P and M are concyclic
b] c]P,L,O,B are con cyclic



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See the diagram.

PQ is parallel to RS in the trapezium.    Given that A is mid point of PR and B is midpoint of QS.     Let C be midpoint of PS and  D be the midpoint of QR.

CB is line joining midpoints of two sides of the triangle PQS.  Hence, CB is parallel to PQ and also PQ = 2 * CB.

Similarly,  in triangle PRS,  CA is parallel to RS, and RS = 2 * CA
           Rs = 2 (CB + BA)  = PQ + 2 BA

         AB = 1/2 * (RS - PQ),           we assumed that RS is bigger than PQ.

If PQ is longer then RS,  then it will be  AB = 1/2 (PQ - RS)
For the  question 2 :
We don't know about the locations points L, M, P and Q,  You need to enclose a diagram.

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