MathDB

Cono Sur Olympiad 2012

Source: Problem 6

November 3, 2012

geometrycircumcirclegeometric transformationreflectionquadraticsgeometry proposed

Problem Statement

6. Consider a triangle

ABC

with

1 < \frac{AB}{AC} < \frac{3}{2}

. Let

M

and

N

, respectively, be variable points of the sides

AB

and

AC

, different from

A

, such that

\frac{MB}{AC} - \frac{NC}{AB} = 1

. Show that circumcircle of triangle

AMN

pass through a fixed point different from

A

.

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