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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