Morley's trisectors

Drag the vertices A, B and C to make the triangle tall, thin or obtuse. Two lines divide each angle into three equal parts; at each side, the two trisectors next to it meet in a point, and the three points P, Q and R make the gold triangle. It turns, grows and shrinks, but the longest side over the shortest, measured in the corner, stays at 1.000000: its three sides are always equal, each 8 sin(A/3) sin(B/3) sin(C/3) times the circumradius. Switch the trisectors to include extra turns: starting from one side and turning by a third of the angle plus an extra 120° or 240°, three turns also land on the other side, so each angle can be trisected three ways and the three angles together 27 ways. Eighteen of them meet in equilateral triangles too, some far outside the triangle; even the worst of the 18 in the corner is 1.000000, and their sides point in only three directions. The other nine make no equilateral triangle and are not drawn. Make the triangle smaller to see more of them.