# 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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by vnikhilesh

2015-03-22T04:20:17+05:30

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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)
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For the  question 2 :
We don't know about the locations points L, M, P and Q,  You need to enclose a diagram.