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# Calculus + Combinatorics = Calculatorics

Points $$P$$ and $$Q$$ are chosen on the two short sides of a right isosceles triangle, one on each side. The perpendiculars $$PM$$ and $$QN$$ are drawn such that $$M$$ and $$N$$ are points on the hypotenuse of the right isosceles triangle. Find the expected value of the area of trapezium $$PMNQ$$, with proof.

Bonus: Generalise this for a right triangle with the two short sides of length $$a$$ and $$b$$.

Note by Sharky Kesa
2 years, 1 month ago

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