MathDB
Geo with unnecessary condition

Source: Turkey Olympic Revenge 2024 P4

August 6, 2024
radical axisgeometry

Problem Statement

Let the circumcircle of a triangle ABCABC be Γ\Gamma. The tangents to Γ\Gamma at B,CB,C meet at point EE. For a point FF on line BCBC which is not on the segment BCBC, let the midpoint of EFEF be GG. Lines GB,GCGB,GC meet Γ\Gamma again at points I,HI,H respectively. Let MM be the midpoint of BCBC. Prove that the points F,I,H,MF,I,H,M lie on a circle.
Proposed by Mehmet Can Baştemir
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