MathDB
Problems
Contests
National and Regional Contests
Peru Contests
Peru Cono Sur TST
2021 Peru Cono Sur TST.
P3
P3
Part of
2021 Peru Cono Sur TST.
Problems
(1)
BFG is a line
Source: Peru Cono Sur TST 2021 #3
8/27/2022
Let
A
B
C
ABC
A
BC
be a triangle and
D
D
D
is a point in
B
C
BC
BC
. The line
D
A
DA
D
A
cuts the circumcircle of
A
B
C
ABC
A
BC
in the point
E
E
E
. Let
M
M
M
and
N
N
N
be the midpoints of
A
B
AB
A
B
and
C
D
CD
C
D
, respectively. Let
F
=
M
N
∩
A
D
F=MN\cap AD
F
=
MN
∩
A
D
and
G
≠
F
G\neq F
G
=
F
is the point of intersection of the circumcircles of
△
D
N
F
\triangle DNF
△
D
NF
and
△
E
C
F
\triangle ECF
△
ECF
. Prove that
B
,
F
B,F
B
,
F
and
G
G
G
are collinears.
geometry
circumcircle