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Most likely point to be enclosed by uniform cevians

Source: Kürschák 2017 Problem 1

October 6, 2017
probabilityPlane GeometryCevas Theoremalgebra

Problem Statement

Let ABCABC be a triangle. Choose points A′A', B′B' and C′C' independently on side segments BCBC, CACA and ABAB respectively with a uniform distribution. For a point ZZ in the plane, let p(Z)p(Z) denote the probability that ZZ is contained in the triangle enclosed by lines AA′AA', BB′BB' and CC′CC'. For which interior point ZZ in triangle ABCABC is p(Z)p(Z) maximised?
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