具有整外半径的Heron等腰
Heron isosceles with integral external radii
摘要：
每个三角形都有三个外圆与包含三角形三条边的三条直线相切，本文推导了三个外圆半径的公式。然后我们将重点放在Heron三角形上。Heron三角形在文献中被称为具有整数边长和整数面积的三角形。毕达哥拉斯三角形是Heron三角形的例子。在本文的第一部分中，我们参数化地描述了所有的Heron等腰三角形。在第二部分中，我们参数化地（根据三个独立的参数）描述了由所有Heron等腰三角形，也有整数外半径的子族。我们提供了数值例子和表格。
英文摘要：
Each triangle has three exterior or external circles tangential to the three straight lines containing the three sides of the triangle.Among the preliminaries in this paper, is deriving formulas for the radii of the three exterior circles in terms of the triangle's sidelengths. After that we focus on Heron triangles. Heron triangles are known in the literature as triangles with integer sidelengths and integral area.Pythagorean triangles are examples of Heron triangles. In the first part of the paper, we parametrically describe all Heron isosceles triangles. In the second part, we parametrically(in terms of three independent parameters) describe the subfamily which consists of all Heron isosceles triangles which also have integral external radii. We provide numerical examples and tables.
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。
