One sphere is centered at $(3,-5,7)$ with radius $5 \sqrt{5}.$  A second sphere is centered at $(0,1,1)$ with radius $2 \sqrt{17}.$  The two spheres intersect in a circle.  Find the radius of this circle.
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One sphere is centered at $(3,-5,7)$ with radius $5 \sqrt{5}.$  A second sphere is centered at $(0,1,1)$ with radius $2 \sqrt{17}.$  The two spheres intersect in a circle.  Find the radius of this circle.
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user
\frac{2 \sqrt{149}}{3}
One sphere is centered at $(3,-5,7)$ with radius $5 \sqrt{5}.$  A second sphere is centered at $(0,1,1)$ with radius $2 \sqrt{17}.$  The two spheres intersect in a circle.  Find the radius of this circle.
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