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The Probability That the Incenter of a Triangle Lies in a Random Diameter Disk
Let $P$ and $Q$ be independent points chosen uniformly from the interior of a nondegenerate triangle $ABC$, and let $I$ be its incenter. We study the probability that the closed disk with diameter $PQ$ contains $I$. In the language of multivariate statistics, this is the spherical depth of $I$ with
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