Problem of Apollonius

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Català: Imatges relacionades amb el problema d'Apol·loni.
English: Images related to the Problem of Apollonius.
Español: Solución al problema de Apolonio.

Sets of eight solutions[edit]

Rescaling circles while preserving tangency[edit]

Intersecting hyperbolae and trilateration[edit]

Descartes' theorem[edit]

Solutions based on circle inversion[edit]

Inversion to two concentric circles[edit]

Gergonne solution[edit]

Lines through tangent points intersect at radical center[edit]

Tangents through tangent points intersect on radical axis of solution pair[edit]

Homothetic axis of given circles equals radical axis of solutions[edit]

Poles of solution radical axis in three given circles[edit]

Ten types of Apollonius' problem[edit]

Type 1: Three points (PPP)[edit]

Type 2: A line and two points (LPP)[edit]

Type 3: Two lines and a point (LLP)[edit]

Type 4: Three lines (LLL)[edit]

Type 5: A circle and two points (CPP)[edit]

Type 6: A circle, a line and a point (CLP)[edit]

Type 7: A circle and two lines (CLL)[edit]

Type 8: Two circles and a point (CCP)[edit]

Type 9: Two circles and a line (CCL)[edit]

Type 10: Three circles (CCC)[edit]

Individual solution pairs[edit]

Individual solutions[edit]

Historical publications[edit]