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Grades 9-10 Video Solutions 2024
2024_9-10_29
2024_9-10_29
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Video Transcription
Video Summary
The problem involves determining the smallest number of distinct lines on a plane, where specific lines intersect a given number of other lines. L1 intersects 5 lines, L2 intersects 9 lines, and L3 intersects 11 lines. Recognizing that a line intersecting 11 others implies a minimum of 12 lines, the proposed solution includes three families: 7 parallel lines, 3 parallel lines, and 2 parallel lines, with each family intersecting the others. This configuration allows L1 to intersect 5 lines, L2 to intersect 9, and L3 to intersect 11, satisfying all conditions. Thus, the minimum value of n is 12.
Keywords
distinct lines
intersection
minimum lines
parallel lines
plane geometry
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