Question

Segment JK is tangent to circle P and circle q, what does JK equal?

Answer 1

I'd be more than happy to do all of that, but I can't even start
until I see YOUR picture of the problem.  That will show me
if circle-P and circle-q are overlapping, just touching, separate
from each other, same size, different sizes, their radii, and where
the points J and K are.  THOSE are the little things I need to know
in order to get started.

You want to know the distance between J and K, but you haven't
given us one single distance or size of anything in the problem ...
nothing at all to work with.  That right there makes it impossible.