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.