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Math: Geometry Problem 1009: Tangent Circles, Common External Tangent, Common Internal Tangent, Arithmetic Mean. Level: School, College.

Circles O and Q are tangent externally at T (see the figure below). If AB and CD are common external tangents and EF is the common internal tangent, prove that EF is the arithmetic mean of AD and BC.
 

Geometry Problem 1009: Tangent Circles, Common External Tangent, Common Internal Tangent, Arithmetic Mean

 


 

 

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Last updated: Sep 19, 2014