The Book of Lemmas: Proposition 6 - Maple Programming Help

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The Book of Lemmas: Proposition 6

Main Concept

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

AC =

CB =

DE =

 

 

 k = ACCB =

 

Therefore:

kk2+k+1 =

DEAB =

ratio ACAB =

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