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Triangle is similar to two others

Source: SMO junior 2024 Q2

October 12, 2024
geometrysimilar trianglesparallelogram

Problem Statement

Let ABCDABCD be a parallelogram and points E,FE,F be on its exterior. If triangles BCFBCF and DECDEC are similar, i.e. △BCF∼△DEC\triangle BCF \sim \triangle DEC, prove that triangle AEFAEF is similar to these two triangles.
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