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Sharygin Geometry Olympiad
2019 Sharygin Geometry Olympiad
20
20
Part of
2019 Sharygin Geometry Olympiad
Problems
(1)
Sharygin CR 2019 P20
Source: Sharygin CR 2019 P20 (Grade 10 - 11)
3/6/2019
Let
O
O
O
be the circumcenter of triangle ABC,
H
H
H
be its orthocenter, and
M
M
M
be the midpoint of
A
B
AB
A
B
. The line
M
H
MH
M
H
meets the line passing through
O
O
O
and parallel to
A
B
AB
A
B
at point
K
K
K
lying on the circumcircle of
A
B
C
ABC
A
BC
. Let
P
P
P
be the projection of
K
K
K
onto
A
C
AC
A
C
. Prove that
P
H
∥
B
C
PH \parallel BC
P
H
∥
BC
.
geometry