MathDB

Two circles meet on AB

Source: Mexico 2023/5

November 8, 2023

geometry

Problem Statement

Let

ABC

be an acute triangle,

\Gamma

is its circumcircle and

O

is its circumcenter. Let

F

be the point on

AC

such that the

\angle COF=\angle ACB

, such that

F

and

B

lie in opposite sides with respect to

CO

. The line

FO

cuts

BC

at

G

. The line parallel to

BC

through

A

intersects

\Gamma

again at

M

. The lines

CO

and

MG

meet at

K

. Show that the circumcircles of the triangles

BGK

and

AOK

meet on

AB

.

Back to Problems View on AoPS