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March 28th, 2018, 02:23 AM   #1
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GF is the radical axis

Given $\Delta ABC$. $D,E$ lie in $AC,AB$. $BD \cap CE =$ {$F$}. $(ADE) \cap (ABC) = ${$G,A$}. Let $M,N,P,Q$ be the midpoint of $BC,ED,EB,CD$, respectively. Prove that $G$F is the radical axis of $(GMN)$ and $(GPQ)$
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