TL;DR
This paper derives the probability distribution and moments of the area of a randomly inscribed triangle within a given triangle, confirmed by Monte Carlo simulations.
Contribution
It provides a novel analytical derivation of the area distribution for inscribed triangles with vertices uniformly chosen on the sides.
Findings
Derived the probability distribution function of the inscribed triangle's area.
Calculated the moments of the area distribution.
Validated results with Monte Carlo simulations.
Abstract
Given a triangle ABC, we derive the probability distribution function and the moments of the area of an inscribed triangle RST whose vertices are uniformly distributed on AB, BC, and CA. The theoretical results are confirmed by a Monte Carlo simulation.
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