An intersection of geometry and combinatorics

Probability Level 4

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 $a + b$ .