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Largest Outscribed Equilateral Triangle

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Phil Todd

@polymnia

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Drag A,B, C to change the original triangle.  Press Play to watch a spring driven equilateral triangle gradually settle at the maximum perimeter position.

Press Show to see the perpendiculars to the sides of the equilateral triangle through A, B and C.

Note that the mechanism settles at a position where these perpendiculars are concurrent.

This is a problem from The Mathematical Gazette March 2014 pp 79-84.

Tags: Fermat, toricelli, equilateral, triangle
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