Sharygin 2006, correspondence round, problem 19
Sharygin 2006, correspondence round, problem 19 is a plane geometry problem from the Sharygin Geometry Olympiad 2006, correspondence round, problem 19 (grades 10–11): lines through the midpoints perpendicular to the bisectors.
Problem
Through the midpoints of the sides of triangle $T$, the lines perpendicular to the bisectors of the opposite angles are drawn. These lines form the triangle $T_1$. Prove that its circumcenter is the midpoint of the segment linking the incenter and the orthocenter of $T$.
Source Sharygin Geometry Olympiad 2006, correspondence round, problem 19 (grades 10–11)
The diagram
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