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National and Regional Contests
Korea Contests
Korea National Olympiad
2020 Korea National Olympiad
2
2
Part of
2020 Korea National Olympiad
Problems
(1)
P,Q,B are collinear
Source: 2020 Korea National Olympiad P2
11/21/2020
H
H
H
is the orthocenter of an acute triangle
A
B
C
ABC
A
BC
, and let
M
M
M
be the midpoint of
B
C
BC
BC
. Suppose
(
A
H
)
(AH)
(
A
H
)
meets
A
B
AB
A
B
and
A
C
AC
A
C
at
D
,
E
D,E
D
,
E
respectively.
A
H
AH
A
H
meets
D
E
DE
D
E
at
P
P
P
, and the line through
H
H
H
perpendicular to
A
H
AH
A
H
meets
D
M
DM
D
M
at
Q
Q
Q
. Prove that
P
,
Q
,
B
P,Q,B
P
,
Q
,
B
are collinear.
geometry
Pascal s theorem