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Apollonius' Tangency Problem For Three Circles. Level: High School, SAT Prep, College geometry

Given three fixed circles, find a circle tangent to all three. The eight solutions are illustrated below. Click the Next button below  to browse through the 10 steps.

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Instructions Next screen: Next button or Right arrow, Previous screen: Previous button or Left arrow, First screen: Up arrow, Last screen: Down Arrow

Apollonius of Perga 262BC - 190BC, Greek mathematician of the Alexandrian school, made historical contributions to mathematics, astronomy and ballistics. His famous book Conics introduced the terms parabola, ellipse and hyperbola. According to Pappus, the Apollonian problem was included in his treatise De Tactionibus ("About Tangencies").

I have used Geometry Expressions to visualize these geometric forms and check out a variety of conjectures. Geometry Expressions is the world's first Interactive Symbolic Geometry System. This means: Geometric figures can be defined by either Symbolic Constraints or numeric locations.

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 See also: 1. Eyeball Theorem: Animated Angle to Geometry Study. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. Monge & d'Alembert Three Circles Theorem II with Dynamic Geometry 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. Proposed Problem 28 Right Triangle, altitude, incircles and inradius. 27. .

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