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Intersections of angle bisectors at A and B and the circle with diameter AB

Source: 2018 Pan-African Shortlist - G4

May 7, 2019
geometryangle bisectorcollinear

Problem Statement

Let ABCABC be a triangle and Γ\Gamma be the circle with diameter [AB][AB]. The bisectors of ∠BAC\angle BAC and ∠ABC\angle ABC cut the circle Γ\Gamma again at DD and EE, respectively. The incicrcle of the triangle ABCABC cuts the lines BCBC and ACAC in FF and GG, respectively. Show that the points D,E,FD, E, F and GG lie on the same line.
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