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Abstract
In any triangle, the perpendicular side bisectors meet the corresponding internal angle bisectors on the circumcircle. If we take those three points as the vertices of a new triangle and repeat the operation indefinitly, we end up in the limit with a par of equilateral triangles whose sides are parallel to the sides of the Morley triangle of the initial triangle.
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Buysse, M. (2020). A New Equilateral Triangle? (arXiv [math.GM] 2007.00448). https://hdl.handle.net/2078.5/167282