MathDB

IMOC 2020 G2 concurency of AO_{An}, BO_{Bn}, CO_{Cn}

Source: https://artofproblemsolving.com/community/c6h2254883p17398793

September 1, 2020

geometryconcurrentconcurrencyCircumcenter

Problem Statement

Let

O

be the circumcenter of triangle

ABC

. Define

O_{A0} = O_{B0} = O_{C0} = O

. Recursively, define

O_{An}

to be the circumcenter of

\vartriangle BO_{A(n-1)}C

. Similarly define

O_{Bn}, O_{Cn}

. Find all

n \ge 1

so that for any triangle

ABC

such that

O_{An}, O_{Bn}, O_{Cn}

all exist, it is true that

AO_{An}, BO_{Bn}, CO_{Cn}

are concurrent.
(Li4)