KöMaL 2008 B4056

The orthocentre of an acute-angled triangle is $M$, the centre of its circumscribed circle is $O$, and its sides are $a$<$b$<$c$. The line of side $c$, the line of the altitude drawn to side $b$, and the line $MO$ form a triangle that is similar to the original triangle but with opposite orientation. Find the angles of the triangle.