An intersection of geometry and combinatorics

Probability Level 4

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

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

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