Dido's Problem/Variant 1/Solution

Solution to Dido's Problem: Variant 1

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.


Sources

  • 1992: David Wells: Curious and Interesting Puzzles ... (previous) ... (next): The Area Enclosed Against The Seashore: $31$
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