2016 OIM Problems/Problem 5
Problem
The circles 
and 
intersect at two different points 
and 
. The tangent
common to and closest to touches at 
and at 
.
Letbe the foot of the perpendicular from
on
, and
the foot of the perpendicular from
on
. If
and
are the symmetrical points of
with respect to the lines
and
, prove that the points
and
be the foot of the perpendicular from 
, and 
the foot of the perpendicular from 
. If 
and 
are the symmetrical points of 
and 
, prove that the points 
and ~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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