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How is a point defined? x,y or ???
How do you compute the "right distance"? How is this point defined?


How do the circles (that implies 2 dimensions) intersect? Wouldn't there be two points...

Do you have the algorithm for the program?
Given that, we can help you write the java program to implement that algorithm.

It looks like you are looking for help with some math concepts and design vs for java programming help.
If you are having problems coding your application in java, please ask your questions here.