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Purple Comet 2017 HS problem 26

Source:

March 19, 2020
geometry

Problem Statement

The incircle of △ABC\vartriangle ABC is tangent to sides BC‾,AC‾\overline{BC}, \overline{AC}, and AB‾\overline{AB} at D,ED, E, and FF, respectively. Point GG is the intersection of lines ACAC and DFDF as shown. The sides of △ABC\vartriangle ABC have lengths AB=73,BC=123AB = 73, BC = 123, and AC=120AC = 120. Find the length EGEG. https://cdn.artofproblemsolving.com/attachments/d/a/aede28071a1a6b94bbe3ad8e1e104822b89439.png
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