We are given $5$ lines and two circles in a plane. What is the maximum number of possible intersection points among these seven figures ?
My work on the problem: I've considered special cases like what is the maximum number of points of intersection between lines and circles ,between only lines and last between circles.
P.s: Please provide detailed answer so i can follow best.Thanks in advance
Best Answer
When you only have 5 lines, you can get at most $\binom{5}{2}=10$ intersections. This is the number of distinct pairs of lines among those five. You can draw it on paper if you don't know the binomial coefficient symbol yet. Each of 2 circles can intersect each of 5 lines at 2 points. There can also be 2 circle-circle intersections.
Line-line intersections: $10$
Line-circle intersections: $2\cdot 2 \cdot 5$
Circle-circle intersections: $2$
Add it up to get the answer.