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National and Regional Contests
Argentina Contests
Argentina Cono Sur TST
2024 Argentina Cono Sur TST
Problem 3
Problem 3
Part of
2024 Argentina Cono Sur TST
Problems
(1)
Circumcenter lies on circumcircle.
Source: Argentina Cono Sur TST 2024 P3
8/9/2024
Let
A
B
C
ABC
A
BC
be an acute triangle. The point
B
′
B'
B
′
of the line
C
A
CA
C
A
is such that
A
A
A
,
C
C
C
,
B
′
B'
B
′
are in that order on the line and
B
′
C
=
A
B
B'C=AB
B
′
C
=
A
B
; the point
C
′
C'
C
′
of the line
A
B
AB
A
B
is such that
A
A
A
,
B
B
B
,
C
′
C'
C
′
are in that order on the line and
C
′
B
=
A
C
C'B=AC
C
′
B
=
A
C
. Show that the circumcenter of triangle
A
B
′
C
′
AB'C'
A
B
′
C
′
belongs to the circumcircle of triangle
A
B
C
ABC
A
BC
.
geometry
circumcircle