2023 AIME I Problems/Problem 3
Problem
A plane contains lines, no of which are parallel. Suppose that there are points where exactly lines intersect, points where exactly lines intersect, points where exactly lines intersect, points where exactly lines intersect, and no points where more than lines intersect. Find the number of points where exactly lines intersect.
Solution
In this solution, let -line points be the points where exactly lines intersect. We wish to find the number of -line points.
There are pairs of lines. Among them:
- The -line points account for pairs of lines.
- The -line points account for pairs of lines.
- The -line points account for pairs of lines.
- The -line points account for pairs of lines.
It follows that the -line points account for pairs of lines, where each pair intersect at a single point.
~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com)
~MRENTHUSIASM
Video Solution by TheBeautyofMath
~IceMatrix
See also
2023 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
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