Problem of Apollonius

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

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Rescaling circles while preserving tangency

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Intersecting hyperbolae and trilateration

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Descartes' theorem

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Solutions based on circle inversion

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Inversion to two concentric circles

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Gergonne solution

Lines through tangent points intersect at radical center

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Tangents through tangent points intersect on radical axis of solution pair

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Homothetic axis of given circles equals radical axis of solutions

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Poles of solution radical axis in three given circles

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Ten types of Apollonius' problem

Type 1: Three points (PPP)

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Type 2: A line and two points (LPP)

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Type 3: Two lines and a point (LLP)

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Type 4: Three lines (LLL)

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Type 5: A circle and two points (CPP)

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

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Type 7: A circle and two lines (CLL)

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Type 8: Two circles and a point (CCP)

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Type 9: Two circles and a line (CCL)

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Type 10: Three circles (CCC)

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Individual solution pairs

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Individual solutions

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Historical publications

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