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Circumcenter becomes orthocenter

Source: Kvant Magazine No. 1 2023 M2732

March 7, 2023

Kvantgeometry

Problem Statement

Let

O{}

be the circumcenter of the triangle

ABC

. On the rays

AC

and

BC

consider the points

C_a

and

C_b

respectively, such that

AC_a

and

BC_b

are equal in length to

AB

. Let

O_c{}

be the circumcenter of the triangle

CC_aC_b

. Define the points

O_a{}

and

O_b{}

similarly. Prove that

O{}

is the orthocenter of the triangle

O_aO_bO_c

.
Proposed by A. Zaslavsky

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