Given a convex polygon with [Formula: see text] vertices, we study the problem of identifying a triangle with its smallest side as large as possible among all the triangles that can be drawn inside the polygon. We show that at least one of the vertices of such a triangle must coincide with a vertex of the polygon. We also propose an [Formula: see text] time algorithm to compute such a triangle inside the given convex polygon.

中文翻译：

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计算凸多边形内最小边长的三角形的高效算法

给定一个带有 [公式：见正文] 顶点的凸多边形，我们研究在所有可以在多边形内绘制的三角形中识别一个最小边尽可能大的三角形的问题。我们证明了这样一个三角形的至少一个顶点必须与多边形的一个顶点重合。我们还提出了一种 [公式：见正文] 时间算法来计算给定凸多边形内的此类三角形。