Miquel's Theorem states that if a point is chosen on each side of a triangle, then the three circles each passing through a vertex and the two chosen points on its adjacent sides all meet at a single common point. Named for Auguste Miquel, it is a classical result of triangle geometry with several later generalizations to complete quadrilaterals and beyond.
Facts
StatementFor a triangle ABC with points on its sides, the three circumcircles through each vertex and two of those points intersect in a single point, the Miquel point. 1 Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Source Miquel's theorem, Wikipedia
Sources
1. Miquel's theorem, Wikipedia
Lead, second paragraph
Miquel's theorem states that these circles intersect in a single point M, called the Miquel point.
In Branch: Geometry, Lead sentence
Miquel's theorem is a result in geometry, named after Auguste Miquel, concerning the intersection of three circles, each drawn thr
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