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We are given a pair of circles in 2D. We have the centre point of both the circles in 2D and its radius. We have to find 2 points P1, P2 such that P1 is on the perimeter of circle A and P2 is on the perimeter of circle B and the distance between them is K.

I came up with an idea of constructing a triangle between C1, P1 and C2 where C1 is centre point of Circle 1, P1 is point on Circle 1 and C2 is centre point of circle 2. But it didn't work.

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  • $\begingroup$ Welcome to MSE. Are you looking for a compass-and-straightedge construction (as your own idea is) or do you welcome any methods including analytic geometric? Please specify that in the post (via clicking the tiny edit) instead of a comment. Also, please learn to use MathJax to properly typeset math. $\endgroup$ – Lee David Chung Lin Oct 13 '18 at 7:06
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I guess this is a problem from live contest . But still I'll give you some hints.

Try to find Minimum and Maximum distance for 3 cases:

  1. Disjoint Circles
  2. Intersecting Circles
  3. One circle Inside another circle

Now all Integer Points in the range [min,max] are points of the circle , so just check the Euclidean distance for each pair in the range and count such points simultaneously.

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