MathDB

8.8

Part of 2023 Sharygin Geometry Olympiad

Problems(1)

locus of common points of lines BC and EF

Source: Sharygin Finals 2023 8.8

8/2/2023
Two circles ω1\omega_1 and ω2\omega_2 meeting at point AA and a line aa are given. Let BCBC be an arbitrary chord of ω2\omega_2 parallel to aa, and EE, FF be the second common points of ABAB and ACAC respectively with ω1\omega_1. Find the locus of common points of lines BCBC and EFEF.
geometrySharygin Geometry OlympiadSharygin 2023