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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/FalseTrue/False

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harshit agarwal , 15 Years ago
Grade 12
anser 1 Answer
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Jitender Singh

Last Activity: 10 Years ago

Ans: True
Let ABCD be a quadrilateral with given sides p, q, r & s in clockwise order.
Area:
Area of triangle ABD + Area of triangle BDC
frac12pq.sinA + frac12rs.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 & Regards
Jitender Singh
IIT Delhi
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