1998 USAMO Problems/Problem 6

Problem

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 $A_{n+j} = A_{j}$ .)

Solution

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1998 USAMO (Problems • Resources)
Preceded by Problem 5	Followed by Last Question
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1998 USAMO Problems/Problem 6

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