Question 8
On the plane, $5$ points $X_1$, $X_2$, $X_3$, $X_4$ and $X_5$ are chosen, and each pair of these points is connected by a blue line. Suppose no two blue lines are parallel or perpendicular to each other. Now for each point $X_i$ $(1\le i\le5)$ and each blue line $L$ not passing through $X_i$, a red line is drawn passing through $X_i$ and perpendicular to $L$. What is the maximum number of points of intersection formed by the red lines?