# Separating line

Two points $$P,Q$$ are chosen uniformly at random from the interior of the square $$ABCD$$. The line $$L_1$$ through $$P$$ and $$Q$$ is drawn. The probability that the points $$A$$ and $$C$$ are on different sides of $$L_1$$ can be expressed as $$\frac{a}{b}$$ where $$a$$ and $$b$$ are coprime positive integers. What is the value of $$a + b$$?

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