設三圓圓心依次為(0,-1),(0,2),(x,y),與三圓相切的圓半徑為k,圓心(a,b),利用連心線長等於半徑和 則x^2+(y-2)^2=(2+3)^2,x^2+(y+1)^2=(1+3)^2 求得(x,y)=(4,-1),(-4,-1) 取(x,y)=(4,-1),同樣利用連心線長等於半徑和 a^2+(b-2)^2=(k+2)^2.......(1) a^2+(b+1)^2=(k+1)^2.......(2) (a-4)^2+(b+1)^2=(k+3)^2.....(3) (1)-(2)得b=-k/3,(2)-(3)得a=-k/2+1 代入(1)得(23k-6)(k+6)=0,故k=6/23或k=-6 k=6/23,與三圓均外切的小圓半徑為6/23 k=-6仍有其幾何意義,代表與三圓均內切的大圓半徑為6
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