MathDB

G4

Part of 2018 Pan-African Shortlist

Problems(1)

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

Source: 2018 Pan-African Shortlist - G4

5/7/2019
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.
geometryangle bisectorcollinear