# An intersection of geometry and combinatorics

Consider a square with vertices $$(0,0), (0,1), (1,1)$$ and $$(1,0)$$. Choose a random point within the square and draw a line segment from it to $$(0,0)$$. Next, choose a second random point within the square and draw a line segment from this point to $$(1,0)$$.

The probability that these two line segments intersect is $$\frac{a}{b}$$, where $$a$$ and $$b$$ are positive coprime integers. Find $$a + b$$.

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