How Many Intersection Points Can Two Circles Have?

hkus10
Messages
50
Reaction score
0
Let C1 and C2 be circles in the plane. Describe the number of possible points of intersection of C1 and C2.

It is 4?
 
Physics news on Phys.org
I don't think I can draw two circles with 4 points of intersection... can you?

Also there are multiple possbilities, there might be 0 for example (just draw one in London and one in Tokyo)
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

Similar threads

Back
Top