1990 OIM Problems/Problem 4
Problem
Let: 
be a circle, 
be one of its diameters, 
be its tangent at 
and 
be a point on other than 
. A circle 
is constructed tangent to at and to the line .
a. Determine the point 
of tangency of and , and find the locus of the centers of the circles by varying .
b. Prove that there is a circle orthogonal to all the circles .
NOTE: Two circles are orthogonal if they intersect and the respective tangents at the points of intersection are perpendicular.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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