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?

Question

08-08-2014
Mathematics

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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?

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Everest2017 Everest2017 · Answer 1 · 2014-08-08T01:46:15-04:00

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.