Six circles theorem
Encyclopedia
In geometry
, the six circles theorem relates to a chain of six circle
s together with a triangle
, such that each circle is tangent
to two sides of the triangle and also to the preceding circle in the chain. The chain closes, in the sense that the sixth circle is always tangent to the first circle.
The name may also refer to Miquel's six circles theorem, the result that if five circles have four triple points of intersection then the remaining four points of intersection lie on a sixth circle.
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, the six circles theorem relates to a chain of six circle
Circle
A circle is a simple shape of Euclidean geometry consisting of those points in a plane that are a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius....
s together with a triangle
Triangle
A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ....
, such that each circle is tangent
Tangent circles
In geometry, tangent circles are circles in a common plane that intersect in a single point. There are two types of tangency: internal and external...
to two sides of the triangle and also to the preceding circle in the chain. The chain closes, in the sense that the sixth circle is always tangent to the first circle.
The name may also refer to Miquel's six circles theorem, the result that if five circles have four triple points of intersection then the remaining four points of intersection lie on a sixth circle.