Monge's Theorem states that for any three circles in a plane, no one lying inside another, the three points where each pair's external common tangent lines cross always lie on a single straight line. Named for Gaspard Monge, it is a classical result of projective and Euclidean geometry proved most directly using the idea of treating the circles as equatorial cross-sections of spheres in three dimensions.
Facts
StatementFor any three circles in a plane, none of which lies completely inside one of the others, the three points where each pair's external tangent lines meet lie on a single straight line. 1 Classification
Statement FormCharacterization Theorem 1 Connections
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Source Monge's theorem, Wikipedia
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Source Monge's theorem, Wikipedia
Sources
1. Monge's theorem, Wikipedia
Lead section, opening sentence
for any three circles in a plane, none of which is completely inside one of the others, the intersection points of each of the three pairs of external tangent lines are collinear.
In Branch: Geometry, Lead sentence
In geometry, Monge's theorem, named after Gaspard Monge, states that for any three circles in a plane, none of which is completely
Proved By: Gaspard Monge, Lead
In geometry, Monge's theorem, named after Gaspard Monge, states that for any three circles in a plane, none of which is completely inside one of the others, the intersection points of each of the three pairs of external tangent lines are collinear
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