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Question
Lines L1,L2,..,L10are distinct among which the lines L2,L4,L6,L8,L10 are
parallel to each other and the lines L1,L3,L5,L7,L9 pass through a given point C. The number of point of intersection of pairs of lines from the complete set L1,L2,L3,...,L10 is
🎥 Video solution / Text Solution of this question is given below:
Total Number of Intersection Points
Given:
- 10 distinct lines: L1,L2,…,L10
- L2,L4,L6,L8,L10: parallel (no intersections among them)
- L1,L3,L5,L7,L9: concurrent at point C (intersect at one point)
? Calculation:
\text{Total line pairs: } \binom{10}{2} = 45
\text{Subtract parallel pairs: } \binom{5}{2} = 10 \Rightarrow 45 - 10 = 35
\text{Concurrent at one point: reduce } 10 \text{ pairs to 1 point} \Rightarrow 35 - 9 = \boxed{26}
✅ Final Answer: \boxed{26} unique points of intersection
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