Question

Lines \( L_1, L_2, \dots, L_{10} \) are distinct, among which the lines \( L_2, L_4, L_6, L_8, L_{10} \) are parallel to each other, and the lines \( L_1, L_3, L_5, L_7, L_9 \) pass through a given point \( C \). The number of points of intersection of pairs of lines from the complete set \( L_1, L_2, L_3, \dots, L_{10} \) is:

• A. 24
• B. 25
• C. 26
• D. 27

Hint:

When counting intersection points, consider parallel lines that do not intersect and focus on lines from different groups or sets. Also, consider points where multiple lines meet.

Answer 1

The Correct Option is C

We have 10 lines in total. Lines \( L_2, L_4, L_6, L_8, L_{10} \) are parallel and do not intersect with each other, while lines \( L_1, L_3, L_5, L_7, L_9 \) are also parallel and do not intersect with each other. Each of the 5 lines from the first group intersects with each of the 5 lines from the second group, leading to \( 5 \times 5 = 25 \) intersection points. Additionally, the 5 lines \( L_1, L_3, L_5, L_7, L_9 \) all intersect at point \( C \), contributing 10 additional intersection points. Thus, the total number of points of intersection is \( 25 + 10 = 26 \).