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Pan African
2024 Pan-African
2
2
Part of
2024 Pan-African
Problems
(1)
Geometry
Source: Pan African Mathematics Olympiad P2
8/15/2024
In triangle
A
B
C
ABC
A
BC
,let
M
M
M
be the midpoint of the side
B
C
BC
BC
,and
N
N
N
is the midpoint of the segment
A
M
AM
A
M
,the circle going through
N
N
N
and tangent the line
A
C
AC
A
C
at
A
A
A
intersects the segment
A
B
AB
A
B
again in
P
P
P
.prove that the circumcircle of triangle
B
P
M
BPM
BPM
is tangent the line
A
M
AM
A
M
geometry
PAMO 2024