A-square-of-edge-lengths-1-has-two-points-A-and-B-with-center-O-A-and-B-are-on-the-perimiter-Area-of-ABO-If-A-and-B-are-random-what-is-the-average-area-of-

Question Number 6676 by FilupSmith last updated on 11/Jul/16

$$\mathrm{A}\:\mathrm{square}\:\mathrm{of}\:\mathrm{edge}\:\mathrm{lengths}\:\mathrm{1}\:\mathrm{has}\:\mathrm{two}\:\mathrm{points} \\ $$$${A}\:\mathrm{and}\:{B},\:\mathrm{with}\:\mathrm{center}\:{O}. \\ $$$${A}\:\mathrm{and}\:{B}\:\mathrm{are}\:\mathrm{on}\:\mathrm{the}\:\mathrm{perimiter}. \\ $$$$\Delta=\mathrm{Area}\:\mathrm{of}\:\bigtriangleup{ABO}. \\ $$$$ \\ $$$$\mathrm{If}\:{A}\:\mathrm{and}\:{B}\:\mathrm{are}\:\mathrm{random},\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{average} \\ $$$$\mathrm{area}\:\mathrm{of}\:\Delta? \\ $$

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