Ta thấy: [tex]\Delta IMN \sim \Delta IFE \Rightarrow \frac{S_{IMN}}{S_{IFE}}=(\frac{IM}{IF})^2\geq 1\Rightarrow S'\geq S_{IFE}[/tex]
Mà [tex]S_{IFE}=\frac{1}{2}.sin\widehat{FIE}.IF.IE=\frac{\sqrt{3}}{4}r^2=\frac{1}{4}S \Rightarrow S' \geq \frac{S}{4} \Rightarrow 4S' \geq S[/tex]