# A question in Permutations and combinations

there are 4 circles and 4 straight lines....find the maximum number of intersecting points possible in the intersection of all these given figures....i cant get how to solve it....

Do you mean the maximum number of points where they all intersect? Or just at least 2 intersect?

A circle can intersect another circle only twice so you would have:
6 intersects + 4 intersects + 2 intersects= 12

A straight line can intersect a circle a maximum of twice and there are four circles so:
8 intersects per line x 4 lines = 32 intersects.

Each line can also intersect the other lines at a single point so they overlap each of the four lines so not recounting an intersect would be:
3+2+1=6

12+32+6= 50 max intersects

Someone should check this ;)

haruspex
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A circle can intersect another circle only twice so you would have:
6 intersects + 4 intersects + 2 intersects= 12

A straight line can intersect a circle a maximum of twice and there are four circles so:
8 intersects per line x 4 lines = 32 intersects.

Each line can also intersect the other lines at a single point so they overlap each of the four lines so not recounting an intersect would be:
3+2+1=6