MathDB

BFG is a line

Source: Peru Cono Sur TST 2021 #3

August 27, 2022

geometrycircumcircle

Problem Statement

Let

ABC

be a triangle and

D

is a point in

BC

. The line

DA

cuts the circumcircle of

ABC

in the point

E

. Let

M

and

N

be the midpoints of

AB

and

CD

, respectively. Let

F=MN\cap AD

and

G\neq F

is the point of intersection of the circumcircles of

\triangle DNF

and

\triangle ECF

. Prove that

B,F

and

G

are collinears.

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