2009 OIM Problems/Problem 3
Problem
Let and
be two circles with centers
and
with the same radius, which intersect at
and
. Let
be a point on the arc
of
that is inside
. Line
intersects
at
, line
intersects
at
and the bisector of
intersects
at
and
at
. Let
be the point symmetrical to
with respect to the midpoint of
. Show that there exists a point
satisfying
and
.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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