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geo... again >:(

Source: MDA TST 2016 P7

March 26, 2019

geometrycircumcircle

Problem Statement

Let

\Omega

and

O

be the circumcircle of acute triangle

ABC

and its center, respectively.

M\ne O

is an arbitrary point in the interior of

ABC

such that

AM

,

BM

, and

CM

intersect

\Omega

at

A_{1}

,

B_{1}

, and

C_{1}

, respectiuvely. Let

A_{2}

,

B_{2}

, and

C_{2}

be the circumcenters of

MBC

,

MCA

, and

MAB

, respectively. It is to be proven that

A_{1}A_{2}

,

B_{1}B_{2}

,

C_{1}C{2}

concur.

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