MathDB

Let

A_1

be the midpoint of the smaller arc

BC

of the circumcircle of the acute-angled triangle

ABC.{}

The point

A_1

is reflected relative to the side

BC,

and then its image is reflected relative to the bisector of

\angle BAC{}

resulting in the point

A_2

. Similarly, the points

B_2

and

C_2

are constructed. Prove that the circumcenter and incenter of the triangle

ABC{}

lie on the Euler line of the triangle

A_2B_2C_2.

Proposed by A. Tereshin

Problem Statement