Li Zhou,
Primitive Heronian triangles with integer inradius and exradii,
Forum Geometricorum, 18 (2018) 71--77.
Abstract. It is well known that primitive Pythagorean triangles have integer
inradius and exradii. We investigate the generalization to prim-
itive Heronian triangles. In particular, we study the special
cases of isosceles triangles and triangles with sides in
arithmetic progression. We also give two families of primitive
Heronian triangles, one decomposable and one indecomposable, which
have integer inradii and exradii. When realized as lattice
triangles, these two families have incenters and excenters at
lattice points as well. Finally we pose two problems for further
research.
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