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Equal Incircles along a Line

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radius
1
number
4
Japanese Sangaku mathematics has a rich history of geometric theorems and problems. The equal incircles theorem is an illustrative example. Consider the incircle
C
of radius
r
of any triangle (each side of the triangle is tangent to the circle) and the extended line
L
along one side of the triangle. Construct a triangle with base common to
L
and an incircle of radius
r
on either side of the triangle. Continue this process on either side of the group of triangles until
n
triangles are constructed,
n>2
. The incircle of the triangle formed by the combination of any
a
,
2≤a<n
, adjacent triangles taken from the group of
n
individual triangles has the same radius as the incircle of the triangle formed by any other
a
adjacent triangles.
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