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The ratio between areas of triangles ABC and DEF

Source: 2022 Abelkonkurransen Finale, Problem 2b

March 12, 2024
geometryareasParallel Lines

Problem Statement

Triangles ABCABC and DEFDEF have pairwise parallel sides: EF∥BC,FD∥CAEF \| BC, FD \| CA, and DE∥ABDE \| AB. The line mAm_A is the reflection of EFEF through BCBC, similarly mBm_B is the reflection of FDFD through CACA, and mCm_C the reflection of DEDE through ABAB. Assume that the lines mA,mBm_A, m_B, and mCm_C meet in a common point. What is the ratio between the areas of triangles ABCABC and DEFDEF?
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