Dido's Problem/Variant 1/Proof 2

Problem

Consider a frame consisting of $4$ rods freely hinged at their ends:

When will the area enclosed by the frame be a maximum?

Solution

When the quadrilateral formed by the frame is cyclic.

Proof

This problem is a direct application of the result:

Area of Quadrilateral with Given Sides is Greatest when Quadrilateral is Cyclic

$\blacksquare$