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Finland Contests
Finnish National High School Mathematics Competition
2014 Finnish National High School Mathematics
2
2
Part of
2014 Finnish National High School Mathematics
Problems
(1)
two circumcirlces given, perpendicularity wanted
Source: Finland 2014, Problem 2
9/1/2019
The center of the circumcircle of the acute triangle
A
B
C
ABC
A
BC
is
M
M
M
, and the circumcircle of
A
B
M
ABM
A
BM
meets
B
C
BC
BC
and
A
C
AC
A
C
at
P
P
P
and
Q
Q
Q
(
P
≠
B
P\ne B
P
=
B
). Show that the extension of the line segment
C
M
CM
CM
is perpendicular to
P
Q
PQ
PQ
.
geometry
circumcircle
perpendicular