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

Let AB, the diameter of a semicircle, be divided at C so that $$\dfrac{AC}{CB}=r$$. If DE is the diameter of the circle inscribed in the arbelos ACB, then $$\dfrac{DE}{AB}=\dfrac{r}{r^2+r+1}$$.
"Arbelos" means shoemaker's knife in Greek.

## Books of Lemmas Index

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