r = raio da circunferência menor
[tex3]\mathsf{
FH \parallel NO, HO \parallel FN, \implies FH = NO\\
Potência ~de~ ponto: FH^2=HC⋅HE\\
3=3⋅(3−2r) \implies r=1\\
\therefore HC⋅(HC+2r)=HF^2\\
HC=1\\
\triangle EFH \sim \triangle CFH:\\
\frac{FC}{FE}=\frac{HC}{FH}\\
FC=\frac{FE}{\sqrt3} \\
T.Pit ~\triangle EFC:\\
2^2=FC^2+FE^2\\
FE=\sqrt3\\
\triangle EFC ~é ~ notável (2,\sqrt3, 1)\implies \angle FCE = 60°\\
S = \frac{120^o⋅π⋅1^2}{360^o}−\frac{1⋅1⋅sen(120^o)}{2}=\boxed{\color{red}\frac{\pi}{3}−\frac{\sqrt3}{4}}
}[/tex3]
(Solução: Ittalo25 -
viewtopic.php?t=89412)