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Problems
Contests
National and Regional Contests
Russia Contests
All-Russian Olympiad Regional Round
2005 All-Russian Olympiad Regional Round
8.4
8.4
Part of
2005 All-Russian Olympiad Regional Round
Problems
(1)
circumcenter of ABC lies on PA All-Russian MO 2005 Regional (R4) 8.4
Source:
8/26/2024
Given an acute triangle
A
B
C
ABC
A
BC
. Points
B
′
B'
B
′
and
C
′
C'
C
′
are symmetrical, respectively, to vertices
B
B
B
and
C
C
C
wrt straight lines
A
C
AC
A
C
and
A
B
AB
A
B
. Let
P
P
P
be the intersection point of the circumcircles of triangles
A
B
B
′
ABB'
A
B
B
′
and
A
C
C
′
ACC'
A
C
C
′
, different from
A
A
A
. Prove that the center of the circumcircle of triangle
A
B
C
ABC
A
BC
lies on line
P
A
PA
P
A
.
geometry
collinear