Jose De la Cruz and John F. Goehl, Jr., Two interesting integer parameters of integer-sided triangles,
Forum Geometricorum, 17 (2017) 411--417.

Abstract. When a triangle is described in terms of the segments into which its sides are divided by an inscribed circle, it permits determination of all integer sided triangles for which the area is an integer multiple of the perimeter. It is not possible to have integer-sided triangles with R/r an integer, where R and r are the radii of the circumcircle and incircle respectively, for right triangles, isosceles triangles, and triangles whose sides are in arithmetic progression. The exception is the equilateral triangle for which R/r = 2.

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