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parallel lines

Source: nigerian mathematics olympiad 3rd round problem 1

February 20, 2020

geometrycircumcircle

Problem Statement

ABC

let

E

and

F

be points on line

AC

and

AB

respectively such that

BE

is parallel to

CF

. suppose that the circumcircle of

BCE

meet

AB

again at

F'

and the circumcircle of

BCF

meets

AC

again at

E'

. show that

BE'

Is parallel to

CF'