Apollonius' Tangency Problem, Circles: College Geometry, SAT Prep. Online Geometry Tutoring

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:

		Eyeball Theorem: Animated Angle to Geometry Study.
		Seven Circles Theorem
		Equal Incircles Theorem
		Tangent Circles Index
		Archimedes' Book of Lemmas
		Butterfly Theorem
		Triangle Centers
		Euler and his beautiful and extraordinary formula
		Semiperimeter and incircle
		Semiperimeter and excircles of a triangle
		Semiperimeter, incircle and excircles of a triangle
		Nagel Point Theorem
		Gergonne Point Theorem
		Monge & d'Alembert Three Circles Theorem I with Dynamic Geometry
		Monge & d'Alembert Three Circles Theorem II with Dynamic Geometry
		Miquel's Pentagram with Dynamic Geometry
		Miquel's Pentagram Theorem. Proof
		Johnson's Theorem
		Simson Line
		Angle between two Simson Lines
		Sangaku Problem
		Newton's Theorem
		The Bevan Point
		Clifford's Circle Chain Theorems
		Kurschak's Tile and Theorem
		Animated Angle to Geometry Study
		Proposed Problem 28 Right Triangle, altitude, incircles and inradius.
		Steiner Point