Differential Calculus> Maxima Minima...

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)

harshit agarwal , 15 Years ago

Grade 12

1 Answers

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

$\frac{1}{2}pq.sinA + \frac{1}{2}rs.sinC$

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 & Regards

Jitender Singh

IIT Delhi

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Differential Calculus> Maxima Minima...

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)

harshit agarwal , 15 Years ago

Jitender Singh

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