MathDB
Question 5

Source: Iran TST 2006

April 18, 2006
geometrycircumcircletrigonometryparallelogramangle bisectorgeometry proposed

Problem Statement

Let ABCABC be a triangle such that it's circumcircle radius is equal to the radius of outer inscribed circle with respect to AA. Suppose that the outer inscribed circle with respect to AA touches BC,AC,ABBC,AC,AB at M,N,LM,N,L. Prove that OO (Center of circumcircle) is the orthocenter of MNLMNL.
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