of the hexagon PQRSTU has a radius of length 1. It is known that PQ = RS = TU = 1.
Let J, K and L correspond respectively to the mid points of the sides QR, ST and UP.
Is it always the case that the triangle JKL is equilateral?
Yes, it's always the case, according to Geometer's Sketchpad, to 8 significant digits, no matter how the three 60-degree chords/arcs are swiveled around.
I have no formal proof.
Posted by Charlie
on 2007-08-01 21:47:29