Finding the Intersection of Two Circles: A Challenge

[mamali]

hi everyone !

we have two circles that doesn't have intersections now we want to find a point on each circle that the distance of this two points are 'k' please help me . . .

 

[tiny-tim]

welcome to pf!

hi everyone !

we have two circles that doesn't have intersections now we want to find a point on each circle that the distance of this two points are 'k' please help me . . .

hi mamali! welcome to pf!

Is this an old-fashioned Euclidean geometry question, or are we allowed to use Cartesian (x and y) coordinates?

Either way, you have to do some of the work yourself …

show us what you've tried. ​

 

[HallsofIvy]

Let the radii of the two circles be $r_1$ and $r_2$ and the distance between the centers be R. Then there cannot be a point on one circle and a point on the other so that the distances between the points is less than $R- (r_1+ r_2)$ nor greater than $R+ (r_1+ r_2)$. Do you see why? For distances between those numbers, as tiny-tim says, we would have to see how you would approach this problem yourself so we can know what kinds of hints will help.