Difference between revisions of "2005 BMO Problems/Problem 1"
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Latest revision as of 16:19, 26 October 2018
Let be an acute-angled triangle whose inscribed circle touches
and
at
and
respectively. Let
and
be the points of intersection of the
bisectors of the angles
and
with
and let
be the midpoint of
.
Prove that the triangle
is equilateral if and only if angle
is equal to
degrees.