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National and Regional Contests
Bosnia Herzegovina Contests
Bosnia Herzegovina Team Selection Test
2017 Bosnia Herzegovina Team Selection Test
6
6
Part of
2017 Bosnia Herzegovina Team Selection Test
Problems
(1)
NIce geometry
Source: Bosnia Herzegovina TST 2017, problem 6
7/24/2017
Given is an acute triangle
A
B
C
ABC
A
BC
.
M
M
M
is an arbitrary point at the side
A
B
AB
A
B
and
N
N
N
is midpoint of
A
C
AC
A
C
. The foots of the perpendiculars from
A
A
A
to
M
C
MC
MC
and
M
N
MN
MN
are points
P
P
P
and
Q
Q
Q
. Prove that center of the circumcircle of triangle
P
Q
N
PQN
PQN
lies on the fixed line for all points
M
M
M
from the side
A
B
AB
A
B
.
geometry
circumcircle