Morley's Trisector Theorem
Morley's trisector theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle, called the first Morley triangle or simply the Morley triangle. No proof provided here, just a graphic. Drag any of the points around to observe that it is true for any triangle. For more information and proofs, see http://en.wikipedia.org/wiki/Morley%27s_trisector_theorem.