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incircle

Source: China south east mathematical olympiad 2006 day2 problem 5

July 4, 2013
geometrytrigonometrysymmetrygeometry unsolved

Problem Statement

In △ABC\triangle ABC, ∠A=60∘\angle A=60^\circ. ⊙I\odot I is the incircle of △ABC\triangle ABC. ⊙I\odot I is tangent to sides ABAB, ACAC at DD, EE, respectively. Line DEDE intersects line BIBI and CICI at FF, GG respectively. Prove that FG=BC2FG=\frac{BC}{2}.
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