MathDB

Cono Sur 2020 Problem 3

Source: Cono Sur Math Olympiad 2020 #3

December 3, 2020

geometrycircumcirclebutterfly theoremcono surlines meeting at circmucirclegeometry solved

Problem Statement

Let

ABC

be an acute triangle such that

AC<BC

and

\omega

its circumcircle.

M

is the midpoint of

BC

. Points

F

and

E

are chosen in

AB

and

BC

, respectively, such that

AC=CF

and

EB=EF

. The line

AM

intersects

\omega

in

D\neq A

. The line

DE

intersects the line

FM

in

G

. Prove that

G

lies on

\omega

.

Back to Problems View on AoPS