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National and Regional Contests
Peru Contests
Peru Iberoamerican Team Selection Test
2010 Peru Iberoamerican Team Selection Test
P3
P3
Part of
2010 Peru Iberoamerican Team Selection Test
Problems
(1)
Determine the locus that determines the circumcenter of triangle ABC as L varies
Source: 2010 Peru Iberoamerican TST problem 3
5/10/2023
Let
C
1
C_1
C
1
and
C
2
C_2
C
2
be two concentric circles with center
O
O
O
, in such a way that the radius of
C
1
C_1
C
1
is smaller than the radius of
C
2
C_2
C
2
. Let
P
P
P
be a point other than
O
O
O
that is in the interior of
C
1
C_1
C
1
, and
L
L
L
a line through
P
P
P
and intersects
C
1
C_1
C
1
at
A
A
A
and
B
B
B
. Ray
O
B
→
\overrightarrow{OB}
OB
intersects
C
2
C_2
C
2
at
C
C
C
. Determine the locus that determines the circumcenter of triangle
A
B
C
ABC
A
BC
as
L
L
L
varies.
geometry