Casey's theorem [SEP] named after
Casey's theorem
In mathematics, Casey's theorem, also known as the generalized Ptolemy's theorem, is a theorem in Euclidean geometry named after the Irish mathematician John Casey.
Formulation of the theorem.
Let formula_1 be a circle of radius formula_2. Let formula_3 be (in that order) four non-intersecting circles that lie inside formula_1 and tangent to it. Denote by formula_5 the length of the exterior common bitangent of the circles formula_6. Then:
Note that in the degenerate case, where all four
- Squircle
- Steiner chain
- Tangential polygon
- Tangential quadrilateral
- Circle-related theory
- Apollonius' problem
- Limiting cases of Apollonius' problem
- Belt problem
- Benz plane
- Bertrand's paradox (probability)
- Bonnesen's inequality
- Brahmagupta's formula
- Buffon's needle problem
- Bundle theorem
- Butterfly theorem
- Carnot's theorem
- Casey's theorem
- Circle graph
- Circle map
- Circle packing
- Circle packing in