Equal Incircles along a Line

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Japanese Sangaku mathematics has a rich history of geometric theorems and problems. The equal incircles theorem is an illustrative example. Consider the incircle of radius
of any triangle (each side of the triangle is tangent to the circle) and the extended line
along one side of the triangle. Construct a triangle with base common to
and an incircle of radius
on either side of the triangle. Continue this process on either side of the group of triangles until
triangles are constructed,
. The incircle of the triangle formed by the combination of any
,
, adjacent triangles taken from the group of
individual triangles has the same radius as the incircle of the triangle formed by any other
adjacent triangles.
Contributed by: Noel Patson (March 2011)
Open content licensed under CC BY-NC-SA
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Inspired by Equal incircles theorem.
Permanent Citation
"Equal Incircles along a Line"
http://demonstrations.wolfram.com/EqualIncirclesAlongALine/
Wolfram Demonstrations Project
Published: March 7 2011