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Problem 366. Scalene triangle, Circumcircle, Angles, 60 Degrees, Equilateral triangle. Level: High School, College, SAT Prep.

The figure shows a triangle ABC inscribed in a circle 1 (circumcircle) and an interior point P so that Angle APB equals angle C plus 60 degrees and Angle BPC equals angle A plus 60 degrees. Lines AP, BP, and CP intersect circle 1 at points D, E, and F, respectively. Prove that triangle DEF is equilateral.

Equilateral triangle, scalene, 60 degree, circumcircle
  
 
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