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IMO ShortList 1998, geometry problem 4

Source: IMO ShortList 1998, geometry problem 4

October 22, 2004
geometryreflectiontrigonometrycircumcircleIMO ShortlistIsogonal conjugate

Problem Statement

Let M M and N N be two points inside triangle ABC ABC such that \angle MAB \equal{} \angle NAC  \mbox{and}  \angle MBA \equal{} \angle NBC. Prove that \frac {AM \cdot AN}{AB \cdot AC} \plus{} \frac {BM \cdot BN}{BA \cdot BC} \plus{} \frac {CM \cdot CN}{CA \cdot CB} \equal{} 1.
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