First excuse my bad drawing. So, Here $\overline{OA} =r,\overline{OB} =2r, \angle{BOE}=\angle{DOE}=\phi, (0<\phi<\pi/2)$. Now I need the 'diameter' of the region shaded in red, where
$\operatorname{diameter}(S)=\sup \{ |x-y|: x,y\in S \}$
for $S\subset \mathbb{R}^2$.
This is used in the 5th chapter of the 'Fractal Geometry' Book by K.Falconer, inside a proof about non-existence of tangent at almost all points of a s-set in $\mathbb{R}^2$, for $1<s<2$. But no explanation is given there and I failed figure it out. Thank you.