Question: Problem 2. Let P be a point inside a triangle ABC. Let D, E, F be reflections of P in the lines BC, CA, AB.

Problem 2. Let P be a point inside a triangle ABC. Let D, E, F be reflections of P in the lines BC, CA, AB. Prove that if the triangle DEF is equilateral, then the lines AD, BE, CF intersect at a common point. Hint: show that the lines AD, BE, CF are bisectors of the sides of the triangle DEF

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