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Korea Junior Mathematics Olympiad
2015 Korea Junior Math Olympiad
1
1
Part of
2015 Korea Junior Math Olympiad
Problems
(1)
Easy Geometry, Colinear Points
Source: 2015 Korean Junior MO P1
11/1/2015
In an acute, scalene triangle
△
A
B
C
\triangle ABC
△
A
BC
, let
O
O
O
be the circumcenter. Let
M
M
M
be the midpoint of
A
C
AC
A
C
. Let the perpendicular from
A
A
A
to
B
C
BC
BC
be
D
D
D
. Let the circumcircle of
△
O
A
M
\triangle OAM
△
O
A
M
hit
D
M
DM
D
M
at
P
(
≠
M
)
P(\not= M)
P
(
=
M
)
. Prove that
B
,
O
,
P
B, O, P
B
,
O
,
P
are colinear.
geometry
circumcircle