Question

Suppose 2 circles are constructed. Under what conditions do the circles have 1 point in common, 2 points in common, no points in common, more than two points in common?

Answer 1

If the two circles are touching tangentially at one point then they have one point in common.  If centers are C1 & C2 and radii are R1 & R2. then  if distance C1C2 = R1+R2 then they have one point in common.


if 0< C1C2  < R1+R2  they are two points in common.
if C1C2 = 0  R1 = R2  then they have all the points in common. they are the same circle.