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Morley triangle with a maximum relative area.

The applet allows to investigate the task : For what type of triangle the Morley triangle gets the maximum relative area ?. One can see that each of the vertices of the triangle can be dragged, and that for each one obtains a triangle , which is the corresponding Morley triangle. In each case the relative area of Morley triangle and the angles of the triangle can be seen on the screen . After dragging the vertices and tracking the relative area one obtains that for an equilateral , the obtained Morley triangle has the maximum relative area.