包含内径和外径的勾股三角形的某些性质
Certain Properties of Pythagorean Triangles involving the interior diameter, and the exterior diameters
摘要：
平面上的每个三角形都有四个特征圆。所有的都与包含三角形三条边的三条直线相切。三是外圆，四是内圆。当三角形是毕达哥拉斯形时，四个直径是整数。考虑一个毕达哥拉斯三角形，它的一个边长是完全（或整数）平方，四个直径中有一个也是整数平方，在八种组合中，我们证明了只有六种是可能的或可能发生的。然后，我们完全参数化地描述了六个家庭;每个家庭对应于六种组合之一。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
