The power of a point is used in many geometrical definitions and proofs.
2.
The \ textstyle n-th power of a point process \ textstyle { N } can be equivalently defined as:
3.
The fundamental purpose of this weapon seems to have been to develop a sling shot with the penetrative power of a point.
4.
As another example, the inscribed angle theorem is the basis for several theorems related to the power of a point with respect to a circle.
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For some integer \ textstyle n = 1, 2, \ dots, the \ textstyle n-th power of a point process \ textstyle { N } is defined as:
6.
In elementary plane geometry, the "'power of a point "'is a real number " h " that reflects the relative distance of a given point from a given circle.
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The power of a point is also known as the point's "'circle power "'or the "'power of a circle "'with respect to the point.
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This definition can be contrasted with the definition of the " n "-factorial power of a point process for which each " n "-tuples consists of " n " points.
9.
For some positive integer \ textstyle n = 1, 2, \ ldots, the \ textstyle n-th factorial power of a point process \ textstyle { N } on \ textstyle \ textbf { R } ^ d is defined as:
10.
In the case when the algebraic curve is a circle this is not quite the same as the power of a point with respect to a circle defined in the rest of this article, but differs from it by a factor of " d " 2.
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