MEMO 2011 ekipno problem 6
Kvaliteta:
Avg: 2.0Težina:
Avg: 6.0 Let
be an acute triangle. Denote by
and
the feet of the altitudes from vertices
and
, respectively. Let
be a point inside the triangle
such that the line
is tangent to the circumcircle of the triangle
and the line
is tangent to the circumcircle of the triangle
. Show that the line
is perpendicular to
.













Source: Srednjoeuropska matematička olimpijada 2011, ekipno natjecanje, problem 6