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        Suppose p,q,r,s are fixed real numbers such that a quadrilateral can be formed with sides p,q,r,s taken in a clockwise order. The vertices of the quadrilateral of maximum area lie on a circle. (True/False)
7 years ago

Jitender Singh
IIT Delhi
158 Points
										Ans: TrueLet ABCD be a quadrilateral with given sides p, q, r & s in clockwise order.Area:Area of triangle ABD + Area of triangle BDC$\frac{1}{2}pq.sinA + \frac{1}{2}rs.sinC$This value will be maximum when the angle A & C are commplementary.$\angle A + \angle C = 180$So the quadrilateral must be cyclic to have max. area.Thanks & RegardsJitender SinghIIT DelhiaskIITians Faculty

2 years ago
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