Distance from point

Dec 2015
975
128
Earth
Given point in space \(\displaystyle P(x_0 , y_0 , z_0 )\) , find the minimal distance between point and sphere: \(\displaystyle (x - a)^2 + (y - b)^2 + (z - c)^2 = r^2\).
 
Mar 2015
182
68
Universe 2.71828i3.14159
The minimal distance between point and sphere lies on a line which passes through the center of the circle. So, find the length of the segment PC (C is the center of the sphere), then subtract r.

$MinimalDistacle=|PC-r|$
 
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Dec 2015
975
128
Earth
The problem looks hard but it is easily solved .:)