11.5

Part of 2001 Saint Petersburg Mathematical Olympiad

Problems(1)

$MI=MH$, where M is the midpoint of arc $AC$

Source: St. Petersburg MO 2001, 11th grade, P5

I

H

be the incenter and orthocenter of an acute triangle

ABC

M

is the midpoint of arc

AC

of circumcircle of triangle

ABC

which does not contain point

B

MI=MH

, find the measure of angle

\angle ABC

.
[I]Proposed by F. Bakharev

geometryorthocenterincentercircumcircle