# A quadrilateralABCD with area2002 contains a point p insideABCD such that PA=24 PB=32 PC=28 PD=45find perimeter of ABCD

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Let diagonals intersect at right angles. Then we have

with equality if  lies on  and  respectively. Thus

Since we have the equality case,  at point

By the Pythagorean Theorem,

The perimeter of  is