Intersecting Lines And Circles

Probability Level 3

The maximum number of points of intersection of 5 straight lines and 4 circles in a plane is $\text{\_\_\_\_\_\_\_\_\_\_}$ .

1 solution

Yash Dev Lamba
Mar 3, 2016

Intersection by Straight lines only $=$ $5\choose 2$ $*1=10$

Intersection by Circles only $=$ $4\choose 2$ $*2=12$

Interseciton by Straight lines and Cricles $=$ $5\choose 1$ $4\choose 1$ $*2=40$

Therefore , Total Number of Intersection are $\boxed{62}$ .

How do you know that such a construction is definitely possible?

(I agree it is somewhat obvious here, but this is an important point of this proof -- all you've technically done is show that 62 is a maximum.)

Eli Ross Staff - 5 years, 3 months ago