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arXiv · 0803.3605

Certain Properties of Pythagorean Triangles involving the interior diameter, and the exterior diameters

Konstantine "Hermes" Zelator
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Abstract

There are four characteristic circles for each triangle on a plane. All for are tangential to the three straight lines containing the triangles' three sides. Three are exterior circles, the fourth is the in-circle. When the triangle is Pythagorean, the four diameters are integers. Consider a Pythagorean triangle with the property that one leglength is a perfect(or integer)square, and with one of the four diameters also a integer square.Of the eight resulting combinations, we prove that only six are possible or can occur. We then completely parametrically describe the six families; each corresponding to one of the six combinations.

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Konstantine "Hermes" Zelator. 2008-03-25. Certain Properties of Pythagorean Triangles involving the interior diameter, and the exterior diameters. https://arxiv.org/abs/0803.3605

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