Difference between revisions of "2009 IMO Problems/Problem 2"
(→Problem) |
m |
||
Line 4: | Line 4: | ||
''Author: Sergei Berlov, Russia'' | ''Author: Sergei Berlov, Russia'' | ||
− | |||
− |
Revision as of 12:03, 10 July 2012
Problem
Let be a triangle with circumcentre
. The points
and
are interior points of the sides
and
respectively. Let
and
be the midpoints of the segments
and
, respectively, and let
be the circle passing through
and
. Suppose that the line
is tangent to the circle
. Prove that
.
Author: Sergei Berlov, Russia