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

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

2008-03-25

arxiv.org/abs/0803.3605v1

Mathematics

General Mathematics

27 pages

Scientific paper

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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