Lines \(L_1, L_2, ..., L_{10}\) are distinct, where lines \(L_2, L_4, L_6, L_8, L_{10}\) are parallel to each other and lines \(L_1, L_3, L_5, L_7, L_9\) pass through a point \(C\). The number of points of intersection of pairs of lines from the set is:
Step-by-step Solution:
1. Parallel lines \( L_2, L_4, L_6, L_8, L_{10} \): These lines are parallel, so no two lines from this group intersect. Therefore, there are no intersections among these 5 lines. \[\] 2. Lines \( L_1, L_3, L_5, L_7, L_9 \) passing through point \( C \): Since all these lines intersect at the single point \( C \), the number of intersections among them is just 1 (they all intersect at \( C \)). \[\] 3. Intersections between the two groups of lines: Each line from the group \( L_1, L_3, L_5, L_7, L_9 \) intersects each line from the group \( L_2, L_4, L_6, L_8, L_{10} \) at a distinct point. There are 5 lines in each group, so the number of intersections between the two groups is: \[ 5 \times 5 = 25 \] Thus, the total number of points of intersection is: \[ 0 + 1 + 25 = 26 \]