The Morley Triangle and Centre

The Morley Centre

The trisectors of the angles of a triangle meet in adjacent pairs that are the vertices of a regular triangle XYZ, called the Morley triangle, whose centre is the Morley centre of the triangle.

The vertices X, Y, Z, are the incentres of the triangles BUC, CVA, AWB, formed by the other pairs of trisectors. The triangles UYZ, VZX, WXY are isosceles.