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Problem 640. Archimedes' Book of Lemmas: Proposition 1.
Level: High School, SAT Prep, College geometry.

1. Internally Tangent Circles at A

If two circles touch at A (internally), and if BC and DE are parallel diameters, then ACE is a straight line.
 

Archimedes Book of Lemmas Internally Tangent Circles 
 

2. Externally Tangent Circles at A

If two circles touch at A (externally), and if BC and DE are parallel diameters, then ACE is a straight line.
 

Archimedes Book of Lemmas Tangent Circles 
 
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