1998 USAMO 第 6 题

Let $n \geq 5$ be an integer. Find the largest integer $k$ (as a function of $n$) such that there exists a convex $n$-gon $A_{1}A_{2}\dots A_{n}$ for which exactly $k$ of the quadrilaterals $A_{i}A_{i+1}A_{i+2}A_{i+3}$ have an inscribed circle. (Here $A_{n+j} = A_{j}$.)

设 $n \geq 5$ 为整数。找到最大整数 $k$(作为 $n$ 的函数)，使得存在一个凸 $n$ 边形 $A_{1}A_{2}\dots A_{n}$，且四边形 $A_{i}A_{i+1}A_{i+2}A_{i+3}$ 中的 $k$ 恰好有一个内接圆。 (这里$A_{n+j} = A_{j}$。)