## Τετάρτη, 11 Οκτωβρίου 2017

### 2006 JBMO Shortlist 11

Circles ${C_1}$ and ${C_2}$ intersect at ${A}$ and ${B}$. Let ${M \in AB}$. A line through ${M}$ (different from ${AB)}$ cuts circles in ${C_1}$ and ${C_2}$ in ${Z,D,E,C}$ respectively such that ${D,E \in ZC}$. Perpendiculars at ${B}$ to the lines ${EB,ZB}$ and ${AD}$ respectively cut circle ${C_2}$ in ${F,K}$ and ${N}$. Prove that ${KF = NC}$.

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