perplexus.info :: Geometry : Take The Midpoints, Get Equilateral?

Take The Midpoints, Get Equilateral? (Posted on 2007-08-01)

The circumcircle 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?

See The Solution Submitted by K Sengupta

Rating: 3.0000 (1 votes)

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answer--but not solution

| Comment 1 of 4

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

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