费尔巴哈定理的一个简单向量证明
A Simple Vector Proof of Feuerbach's Theorem
摘要：
著名的费尔巴哈定理指出，一个不等边三角形的九点圆与它的内圆和三个外圆都相切。本文用简单的向量计算给出了费尔巴哈定理的一个简单证明。为了完整起见，这里证明了所有必需的参数。
英文摘要：
The celebrated theorem of Feuerbach states that the nine-point circle of a nonequilateral triangle is tangent to both its incircle and its three excircles. In this note, we give a simple proof of Feuerbach's Theorem using straightforward vector computations. All required preliminaries are proven here for the sake of completeness.
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。
