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CircleThrough[{p1,p2,…}]

represents a circle passing through the points pi.

CircleThrough[{p1,p2,…},q]

represents a circle with center q.

CircleThrough[{p1,p2,…},q,r]

represents a circle with radius r.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Properties & Relations  
Possible Issues  
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CircleThrough

CircleThrough[{p1,p2,…}]

represents a circle passing through the points pi.

CircleThrough[{p1,p2,…},q]

represents a circle with center q.

CircleThrough[{p1,p2,…},q,r]

represents a circle with radius r.

Details

Examples

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Basic Examples  (2)

A circle passing through three points:

Wolfram Language code: pts = {{0, 0}, {1, 0}, {0, 1}};
Wolfram Language code: CircleThrough[pts]
Wolfram Language code: Graphics[{%, Red, Point[pts]}]

ArcLength of an circle passing through a set of points:

Wolfram Language code: pts = {{(1/2), (Sqrt[3]/2)}, {-(1/2), (Sqrt[3]/2)}, {-1, 0}};
Wolfram Language code: ArcLength[CircleThrough[pts]]

Scope  (3)

CircleThrough works on lists of coordinates:

Wolfram Language code: CircleThrough[{{0, 0}, {1, 0}, {0, 1}}]

A circle passing through a list of points with a given center and radius:

Wolfram Language code: CircleThrough[{{0, 0}, {1, 0}, {0, 1}}, {1 / 2, 1 / 2}, 1 / Sqrt[2]]

CircleThrough works in GeometricScene:

Wolfram Language code: RandomInstance[GeometricScene[{a, b, c}, {CircleThrough[{a, b, c}], CircleThrough[{a, b}, c, 3]}]]

Properties & Relations  (5)

CircleThrough returns a Circle:

Wolfram Language code: CircleThrough[{{0, 0}, {1, 0}, {0, 1}}]

Use RegionMember to test point membership:

Wolfram Language code: reg = CircleThrough[{{0, 0}, {1, 0}, {0, 1}}]
Wolfram Language code: RegionMember[reg, {0, 0} ]
Wolfram Language code: RegionMember[reg, {-1, 1} ]

Use RegionFit to find a circle that fits a set of points:

Wolfram Language code: points = CirclePoints[5];
Wolfram Language code: RegionFit[points, "Circle"]

The circle passing the first 3 points:

Wolfram Language code: CircleThrough[Take[points, 3]]

Use CirclePoints to generate equally spaced points on the unit circle:

Wolfram Language code: pts = CirclePoints[3]

The unit circle:

Wolfram Language code: CircleThrough[pts]

Use CircleThrough to specify hypotheses in GeometricScene:

Wolfram Language code: RandomInstance[GeometricScene[{a, b, c}, {CircleThrough[{a, b, c}], CircleThrough[{a, b}, c, 3]}]]

Possible Issues  (1)

CircleThrough returns unevaluated if the points are not explicit:

Wolfram Language code: CircleThrough[{a, b, c}]
Wolfram Research (2019), CircleThrough, Wolfram Language function, https://reference.wolfram.com/language/ref/CircleThrough.html.

Text

Wolfram Research (2019), CircleThrough, Wolfram Language function, https://reference.wolfram.com/language/ref/CircleThrough.html.

CMS

Wolfram Language. 2019. "CircleThrough." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CircleThrough.html.

APA

Wolfram Language. (2019). CircleThrough. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CircleThrough.html

BibTeX

@misc{reference.wolfram_2026_circlethrough, author="Wolfram Research", title="{CircleThrough}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/CircleThrough.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_circlethrough, organization={Wolfram Research}, title={CircleThrough}, year={2019}, url={https://reference.wolfram.com/language/ref/CircleThrough.html}, note=[Accessed: 13-June-2026]}