A, A', A'' are points on the circumcircle of a triangle t1, so that the triangle (AA'A'') is equilateral. Then the triangle (XYZ) of the intersection-points of their corresponding Simson-Wallace lines (see Simson.html ) is equilateral.
a) When this triangle is degenerate (then X, Y, Z coincide with the center of the Euler circle of t1), then the corresponding Simson-lines are parallel to the sides of the Morley-Triangle.
b) When this triangle is maximal, then its sides are parallel to the sides of (AA'A''), it is even circumscribed on the Euler circle of t1. In addition, its sides are again parallel to the Morley's sides.
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A property of Simson-Wallace Lines ![[0_0]](Simson_3Lines_files/Simson_3Lines_0_0_0.png)
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![[1_1]](Simson_3Lines_files/Simson_3Lines_0_1_1.png)
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![[1_3]](Simson_3Lines_files/Simson_3Lines_0_1_3.png)