绘制共斜边模型的外接球？

\documentclass{standalone}
\usepackage[3d]{luadraw}
\usepackage[svgnames]{xcolor}
\usepackage{fourier-otf}
\begin{document}
    \begin{luadraw}{name=spherical_circle}
    local ld = luadraw
    local pt3d, cpx = ld.pt3d, ld.cpx
    local M, Mc, Ms = pt3d.M, pt3d.Mc, pt3d.Ms
    local Origin, vecI, vecJ, vecK = pt3d.Origin, pt3d.vecI, pt3d.vecJ, pt3d.vecK
    local g = ld.graph3d:new{
        window3d = {-5,5,-5,5,-5,5},
        window = {-5,5,-5,5},
        -- adjust2d = true, 
        viewdir = {0,65}
    }
    require 'luadraw_spherical'
    local sM = ld.sM
    ld.Hiddenlines = true;ld.Hiddenlinestyle = "dashed"
    g:Define_sphere{ color = "", edgewidth=8, edgecolor="black" }
    local A,B,C,D = sM(90,90), sM(140,90),sM(-40,90), sM(-120,50)
    g:DScircle({Origin, vecK})
    local vecn = pt3d.prod(B,D)
    g:Dcircle3d(Origin,3,vecn,"draw=none, fill=violet!30, fill opacity=0.4")
    g:DSgreatcircle({B,D},{width = 6})
    g:Dspherical()
    g:Dpolyline3d({{A,B,D,C,A},{A,D},{B,C}},"dashed,red,thick")
    g:Dpolyline3d({D,Origin,A},"dashed,blue!75,thick")
    g:Dballdots3d({Origin,A,B,C,D},"red",0.75)
    g:Dlabel3d(
        "$O$",Origin,{pos="S"},
        "$C$",C,{pos="SW"},
        "$B$",B,{pos="NE"},
        "$D$",D,{pos="N"},
        "$A$",A,{pos="E"},
        "$r$",A/2,{pos="N",node_options="text=blue"},
        "$r$",D/2,{pos="S",dist=0.1},
        "$\\ell$",Origin,{pos="N",node_options="text=red"}
    )
    g:Show()
\end{luadraw}
\end{document}