The Book of Lemmas: Proposition 6
Let AB, the diameter of a semicircle, be divided at point C so that ACCB = k. If DE is the diameter of the circle inscribed in the arbelos which is tangent to all three semicircles, then DEAB = kk2+k+1 .
Adjust the slider, or click and drag on the plot to change the ratio of ACAB. Observe the values on the right which validate this proposition.
AB = 2
k = ACCB =
ratio ACAB =
Download Help Document