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locus of common points of lines BC and EF

Source: Sharygin Finals 2023 8.8

August 2, 2023

geometrySharygin Geometry OlympiadSharygin 2023

Problem Statement

Two circles

\omega_1

and

\omega_2

meeting at point

A

and a line

a

are given. Let

BC

be an arbitrary chord of

\omega_2

parallel to

a

, and

E

,

F

be the second common points of

AB

and

AC

respectively with

\omega_1

. Find the locus of common points of lines

BC

and

EF

.

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