Τρίτη, 17 Οκτωβρίου 2017

2002 IMO Shortlist G8

Let $S_1$ and $S_2$ be circles meeting at the points $A$ and $B$. A line through $A$ meets $S_1$ at C and $S_2$ at $D$. Points $M, N, K$ lie on the line segments $CD, BC, BD$ respectively, with $MN$ parallel to $BD$ and $MK$ parallel to $BC$. Let $E$ and $F$ be points on those arcs $BC$ of $S_1$ and $BD$ of $S_2$ respectively that do not contain $A$. Given that $EN$ is perpendicular to $BC$ and $FK$ is perpendicular to $BD$ prove that $\angle EMF = 90^\circ$ .

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