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KoMaL A Problems
KoMaL A Problems 2022/2023
A. 831
A. 831
Part of
KoMaL A Problems 2022/2023
Problems
(1)
Nice Collinearity
Source: KöMaL A. 831
10/11/2022
In triangle
A
B
C
ABC
A
BC
let
F
F
F
denote the midpoint of side
B
C
BC
BC
. Let the circle passing through point
A
A
A
and tangent to side
B
C
BC
BC
at point
F
F
F
intersect sides
A
B
AB
A
B
and
A
C
AC
A
C
at points
M
M
M
and
N
N
N
, respectively. Let the line segments
C
M
CM
CM
and
B
N
BN
BN
intersect in point
X
X
X
. Let
P
P
P
be the second point of intersection of the circumcircles of triangles
B
M
X
BMX
BMX
and
C
N
X
CNX
CNX
. Prove that points
A
,
F
A, F
A
,
F
and
P
P
P
are collinear.Proposed by Imolay András, Budapest
geometry
komal