Pollock

Pollock's configuration

Start with a right angled triangle DEF.
On the three arcs of its circumcircle take three points correspondingly H, I and J.
Draw the tangents to the circumcircle at these points.
Find the midles A, C, B correspondingly, of the segments cut on these tangents by the (prolongations of) sides of the right angle.
The red curve "c" is the locus of these midle-points as the tangent takes various positions.
Pollock's theorem says that when the 3 identifications occur simultaneously:
A and H coincide (with the point of tangency of the arc AF with c),
C and I coincide (with the point of tangency of the arc DF with c),
B and J coincide (with the point of tangency of the arc ED with c),
then the triangle ABC is equilateral.

To see it experimentaly, switch to the "Selection on Contour" (press Ctrl+2) and move the points H, I, J until to achieve the above coincidences. Then look at the measures of the angles A, B, C , displayed above.
For a precise construction of "Polock's equilateral triangle" look at the file [ Pollock2.html ].

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