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equilaterals, \frac{|DB|}{|DC|} = \frac{|EC|}{|EA|} = \frac{|FA|}{|FB|}

Source: Polish MO Recond Round 1991 p2

September 9, 2024
geometryEquilateral

Problem Statement

On the sides BC BC , CA CA , AB AB of the triangle ABC ABC , the points D D , E E , F F are chosen respectively, such that ∣DB∣∣DC∣=∣EC∣∣EA∣=∣FA∣∣FB∣ \frac{|DB|}{|DC|} = \frac{|EC|}{|EA|} = \frac{|FA|}{|FB|} Prove that if the triangle DEF DEF is equilateral, then the triangle ABC ABC is also equilateral.
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