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 Seven Circles  Theorem. Variants 1, 2, and 3. Level: High School, SAT Prep, College geometry

Draw a circle and arrange six circles tangent to it such that they touch both the original circle and their two neighbors. Then the three lines joining opposite points of tangency concur. 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

Reference: Evelyn, C. J. A., Money-Coutts, G. B. & Tyrrell, J. A. (1974), The Seven Circles Theorem and other New Theorems, Stacey International, London

 

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.

You can download Geometry Expressions 1.0 Free Trial. It is a fully featured 30 day evaluation copy of the software. All constraints, constructions and measurements are available for you to use.
 

 

 
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Last updated: March 1, 2008