October 10th, 2019, 03:01 AM  #1 
Senior Member Joined: Dec 2015 From: somewhere Posts: 734 Thanks: 98  Distance from point
Given point in space $\displaystyle P(x_0 , y_0 , z_0 )$ , find the minimal distance between point and sphere: $\displaystyle (x  a)^2 + (y  b)^2 + (z  c)^2 = r^2$.

October 10th, 2019, 03:21 AM  #2 
Senior Member Joined: Mar 2015 From: Universe 2.71828i3.14159 Posts: 132 Thanks: 49 Math Focus: Area of Circle 
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. $MinimalDistacle=PCr$ Last edited by skipjack; October 10th, 2019 at 06:39 AM. 
October 10th, 2019, 03:59 AM  #3 
Senior Member Joined: Dec 2015 From: somewhere Posts: 734 Thanks: 98 
The problem looks hard but it is easily solved . 

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distance, point 
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