Question:
The greatest possible number of points of intersection of 8 distinct straight lines and 4 distinct circles is
The greatest possible number of points of intersection of 8 distinct straight lines and 4 distinct circles is
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Count intersection points for each pair type: line-line, circle-circle and line-circle.
Updated On: Nov 13, 2026
- 28
- 104
- \({}^{12}\mathrm{C}_{2}\)
- \({}^{4}\mathrm{C}_{2}\)
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept
Two lines meet in at most 1 point. Two circles meet in at most 2 points. A line and a circle meet in at most 2 points.
Step 2: Line-Line
\({}^{8}\mathrm{C}_{2}\times1=28\).
Step 3: Circle-Circle and Line-Circle
Circle-circle: \({}^{4}\mathrm{C}_{2}\times2=12\).
Line-circle: \(8\times4\times2=64\).
Step 4: Total
\(28+12+64=104\), option (B).
Final Answer:
The greatest number of intersection points is 104. \[ \boxed{\text{(B) }104} \]
Two lines meet in at most 1 point. Two circles meet in at most 2 points. A line and a circle meet in at most 2 points.
Step 2: Line-Line
\({}^{8}\mathrm{C}_{2}\times1=28\).
Step 3: Circle-Circle and Line-Circle
Circle-circle: \({}^{4}\mathrm{C}_{2}\times2=12\).
Line-circle: \(8\times4\times2=64\).
Step 4: Total
\(28+12+64=104\), option (B).
Final Answer:
The greatest number of intersection points is 104. \[ \boxed{\text{(B) }104} \]
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