What the formula for the distance from a point to a sphere

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SUMMARY

The formula for calculating the distance from a point to a sphere is derived from the distance to the center of the sphere. If the point is outside the sphere, the distance is calculated by finding the distance from the point to the center of the sphere and then subtracting the sphere's radius. Conversely, if the point is inside the sphere, the radius is subtracted from the distance to the center, and the absolute value is taken to ensure a non-negative result. This method provides a clear and definitive approach to determining the distance in both scenarios.

PREREQUISITES
  • Understanding of Euclidean geometry
  • Familiarity with the distance formula in three-dimensional space
  • Knowledge of sphere properties, including radius and center
  • Basic algebra for manipulating equations
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khdani
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i know this formula from a point to a plane
<br /> d=\frac{Ax_0+By_0+cz_0}{\sqrt{A^2+B^2+C^2}}<br />

and i know that i could take from its center.

but i am looking for a formula of the distance from a point to a sphere
??
 
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I'm not aware that there is such a formula, at least not one that is widely circulated. Assuming the point is outside the sphere, find the distance from the point to the center of the sphere, and then subtract the radius of the sphere.
 
If the point is inside the sphere, do the subtraction the other way around. Or, like you do with the distance between two points on a number line, do the subtraction either way and take the absolute value.
 

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