Problem 645: Archimedes' Book of Lemmas: Proposition 6, Arbelos

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Let AB, the diameter of a semicircle, be divided at C so that Diameters. If DE is the diameter of the circle inscribed in the arbelos ACB, then Formula to prove.
"Arbelos" means shoemaker's knife in Greek.
 

Arimedes Lemma 6, Arbelos and Inscribed circle
 
 

Lemma 6 with Archimedes as shown in 1584 book by Andre Thevet in the background

Archimedes Lemma 6, Arbelos and Inscribed circle, Archimedes in the background
  

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