# Equal Incircles along a Line

Equal Incircles along a Line

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.

C

r

L

L

r

n

n>2

a

2≤a<n

n

a