圆、三角形是几何的基本图形,也是我们认识许多其他图形的基础．三角形与圆的关系一般研究、讨论较多的是三角形与它的内切圆的关系与性质,三角形与它的外接圆的关系与性质,或三角形一条边与一个圆外切的关系与性质,而同时讨论三角形的三条边与三个外切圆的关系则较少涉及到,经过探讨,笔者推导一个三角形三边与它们的外切圆关系的结果并证明之． Circles and triangles are basic geometric shapes, and they are the basis for many other graphics. The relationship between triangles and circles is generally studied and discussed. The relationship and nature of triangles to their inscribed circles, the relationship and nature of triangles to their circumscribed circles, or the relationship and nature of one side of a triangle to the outer circle of a circle. At the same time, the relationship between the three sides of the triangle and the three circumscribed circles is less involved. After discussion, the author deduces the results of a relationship between three sides of a triangle and their tangent circles and proves it.