1996 OIM Problems/Problem 2
Problem
Let 
be the midpoint of the median 
of triangle 
(
belongs to side 
). The line 
cuts the side 
at the point 
. Prove that 
is tangent to the circumcircle of the triangle 
if, and only if, the following equality is verified
![\[\frac{\overline{BM}}{\overline{MN}} = \frac{(\overline{BC})^2}{(\overline{BN})^2}\]](http://latex.artofproblemsolving.com/7/5/6/7564528e92e1b0167896fc0092fd4b83e107183e.png)
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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