2013 OIM Problems/Problem 2
Problem
Let ,
be the ends of a diameter of a circle
and
the the midpoint of one of the
arcs of
. Let
and
be two points on the segment
. The straight lines
and
cut
again at points
and
, respectively. The tangents to
in
and
intersect at
. Let
be the point of intersection of segment
with segment
. Show that
is the midpoint of segment
.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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