MathDB

The points

A_1

B_1

C_1

are middle points of the arcs

\widehat{BC}, \widehat{CA}, \widehat{AB}

of the circumscribed circle of

\Delta ABC

, respectively. The points

I_a,I_b,I_c

are the reflections in the middle points of

BC,CA,AB

of the center

I

of the inscribed circle in the triangle. Prove that

I_a A_1,I_b B_1

, and

I_c C_1

are concurrent.

Problem Statement