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Sharygin CR 2019 P17

Source: Sharygin CR 2019 P17 (Grade 10 - 11)

March 6, 2019

geometry

Problem Statement

Three circles

\omega_1

,

\omega_2

,

\omega_3

are given. Let

A_0

and

A_1

be the common points of

\omega_1

and

\omega_2

,

B_0

and

B_1

be the common points of

\omega_2

and

\omega_3

,

C_0

and

C_1

be the common points of

\omega_3

and

\omega_1

. Let

O_{i,j,k}

be the circumcenter of triangle

A_iB_jC_k

. Prove that the four lines of the form

O_{ijk}O_{1 - i,1 - j,1 - k}

are concurrent or parallel.

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