When an angle in triangle
ABC is larger than 120 degrees, the lines created by the equilateral
triangles are not concurrent. In the picture below, angle ACB
is greater than 120 degrees. If P was located at the point of
intersection of DB and AG, the distance AP would be greater than
the distance AC, as would the distance BP be greater than the
distance BC. Therefore, when this is the case, P is located on
the vertex of the angle that is larger than 120 degrees.
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