Expected Area

Geometry Level 3

Triangle ABCABC has side lengths BC=13,CA=14,AB=15 BC = 13, CA = 14, AB = 15. A point PP is selected at random from the interior of the triangle and the line APAP is extended to meet BCBC at the point QQ. What is the expected value of [ABQ][ABQ]?

Details and assumptions

[PQRS][PQRS] denotes the area of figure PQRSPQRS.

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