RU-ALLRUSSIAN 1985 Problem 1
ABC is an acute angled triangle. The midpoints of BC, CA and AB are D, E, F respectively. Perpendiculars are drawn from D to AB and CA, from E to BC and AB, and from F to CA and BC. The perpendiculars form a hexagon. Show that its area is half the area of the triangle.
Dataset text NuminaMath olympiads. Quoted with source.
Solutions
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