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SMT RMT 2014 Geometry #10

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October 28, 2022
geometry

Problem Statement

Let ABCABC be a triangle with AB=12AB = 12, BC=5BC = 5, AC=13AC = 13. LetD D and EE be the feet of the internal and external angle bisectors from BB, respectively. (The external angle bisector from BB bisects the angle between BCBC and the extension of ABAB.) Let ω\omega be the circumcircle of △BDE\vartriangle BDE, extend ABAB so that it intersects ω\omega again at FF. Extend FCF C to meet ω\omega again at XX, and extend AXAX to meet ω\omega again at GG. Find FGF G.
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