Kira Adaricheva和Madina Bolat关于凸性和圆的一个定理的简便证明
An easy way to a theorem of Kira Adaricheva and Madina Bolat on convexity and circles
摘要：
Kira Adaricheva和Madina Bolat最近证明了，如果$U_0$和$U_1$是三角形中的圆，顶点为$A_0,A_1,A_2$，则存在$j\in \{0,1,2\}$和$k\in\{0,1\}$，使得$U_{1-k}$包含在$U_k\cup(\{A_0,A_1, A_2\}\setminus\{A_j\})$的凸包中。我们给这个结果一个简短的新的证明，我们指出，一个简单的推广shperes失败。
英文摘要：
Kira Adaricheva and Madina Bolat have recently proved that if $U_0$ and $U_1$ are circles in a triangle with vertices $A_0,A_1,A_2$, then there exist $j\in \{0,1,2\}$ and $k\in\{0,1\}$ such that $U_{1-k}$ is included in the convex hull of $U_k\cup(\{A_0,A_1, A_2\}\setminus\{A_j\})$. We give a short new proof for this result, and we point out that a straightforward generalizaton for shperes fails.
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。
