Power of a Point with Respect to a Sphere

Rarely Tested

Power of a Point with Respect to a Sphere

For sphere:

$$(x-a)^2+(y-b)^2+(z-c)^2=r^2$$

and point $$P(x_1,y_1,z_1)$$, the power is:

$$PC^2-r^2$$

Usage

- Used to determine whether a point lies inside, on, or outside a sphere and to study tangent lengths.

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