# Expected Area

Geometry Level 3

Triangle $$ABC$$ has side lengths $$BC = 13, CA = 14, AB = 15$$. A point $$P$$ is selected at random from the interior of the triangle and the line $$AP$$ is extended to meet $$BC$$ at the point $$Q$$. What is the expected value of $$[ABQ]$$?

Details and assumptions

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

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