Five circles theorem
Derives a pentagram from five chained circles centered on a common sixth circle
title: "Five circles theorem" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["theorems-about-circles"] description: "Derives a pentagram from five chained circles centered on a common sixth circle" topic_path: "general/theorems-about-circles" source: "https://en.wikipedia.org/wiki/Five_circles_theorem" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0
::summary Derives a pentagram from five chained circles centered on a common sixth circle ::
::figure[src="https://upload.wikimedia.org/wikipedia/commons/5/52/Five_circles_theorem.svg"] ::
In geometry, the five circles theorem states that, given five circles centered on a common sixth circle and intersecting each other chainwise on the same circle, the lines joining their second intersection points forms a pentagram whose points lie on the circles themselves.
References
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