MathDB

2

Part of 1991 Poland - Second Round

Problems(1)

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

Source: Polish MO Recond Round 1991 p2

9/9/2024
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.
geometryEquilateral