MathDB

11

Part of 2014 Baltic Way

Problems(1)

Equal segments

Source: Baltic Way 2014, Problem 11

11/11/2014
Let Γ\Gamma be the circumcircle of an acute triangle ABC.ABC. The perpendicular to ABAB from CC meets ABAB at DD and Γ\Gamma again at E.E. The bisector of angle CC meets ABAB at FF and Γ\Gamma again at G.G. The line GDGD meets Γ\Gamma again at HH and the line HFHF meets Γ\Gamma again at I.I. Prove that AI=EB.AI = EB.
geometrycircumcirclegeometric transformationreflectiongeometry proposed