A sphere intersects the $xy$-plane in a circle centered at $(2,4,0)$ with radius 1.  The sphere also intersects the $yz$-plane in a circle centered at $(0,4,-7),$ with radius $r.$  Find $r.$
<|im_start|>system
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<|im_start|>user
A sphere intersects the $xy$-plane in a circle centered at $(2,4,0)$ with radius 1.  The sphere also intersects the $yz$-plane in a circle centered at $(0,4,-7),$ with radius $r.$  Find $r.$
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<|im_start|>assistant

user
\sqrt{46}
A sphere intersects the $xy$-plane in a circle centered at $(2,4,0)$ with radius 1.  The sphere also intersects the $yz$-plane in a circle centered at $(0,4,-7),$ with radius $r.$  Find $r.$
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