MathDB
JBMO Shortlist 2023 G7

Source: JBMO Shortlist 2023, G7

June 28, 2024
JBMOJBMO Shortlistgeometry

Problem Statement

Let DD and EE be arbitrary points on the sides BCBC and ACAC of triangle ABCABC, respectively. The circumcircle of △ADC\triangle ADC meets for the second time the circumcircle of △BCE\triangle BCE at point FF. Line FEFE meets line ADAD at point GG, while line FDFD meets line BEBE at point HH. Prove that lines CF,AHCF, AH and BGBG pass through the same point.
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