Question 1056900
Begin making a graph according to this description to help see what you may be able to do:

Circle centered at origin (0,0) and radius 2;
Point for other circle center at (4,3), but radius is unknown, k.
A segment connects the two center points (0,0) and (4,3).  The equation for the LINE for this segment is  {{{y=(3/4)x}}}.


THINK about that, and the drawing you hopefully made.
Do you imagine a process to continue and find your k?  
As a big hint toward that, What is the intersection point for {{{y=(3/4)x}}} and {{{x^2+y^2=4}}}?


What is the distance between that found intersection point and (4,3)?
That would be k.



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I did not solve this for you but explained precisely how you can solve it.


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Solving the nonlinear system  {{{system(y=(3/4)x,x^2+y^2=4)}}}, omitting the steps for it here, should give you the intersection point, ( 8/5, 6/5 ).  Use the distance formula to find distance from  ( 8/5, 6/5)  to (4,3).  That is your k.