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Determine the locus that determines the circumcenter of triangle ABC as L varies

Source: 2010 Peru Iberoamerican TST problem 3

May 10, 2023

geometry

Problem Statement

Let

C_1

and

C_2

be two concentric circles with center

O

, in such a way that the radius of

C_1

is smaller than the radius of

C_2

. Let

P

be a point other than

O

that is in the interior of

C_1

, and

L

a line through

P

and intersects

C_1

A

and

B

. Ray

\overrightarrow{OB}

intersects

C_2

C

. Determine the locus that determines the circumcenter of triangle

ABC

L

varies.