View source for 1985 OIM Problems/Problem 6

== Problem ==
Given triangle <math>ABC</math>, we consider the points <math>D</math>, <math>E</math>, and <math>F</math> of lines <math>BC</math>, <math>AC</math>, and <math>AB</math> respectively.  If lines <math>AD</math>, <math>BE</math>, and <math>CF</math> all pass through the center <math>O</math> of the circumference of triangle <math>ABC</math>, which radius is <math>r</math>, prove:
<cmath>\frac{1}{AD}+\frac{1}{BE}+\frac{1}{CE}=\frac{2}{r}</cmath>

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

== Solution ==
{{solution}}

== See also ==
https://www.oma.org.ar/enunciados/ibe1.htm