SOLUTION: Two circles lying in the first quadrant, touch each other externally. Both the axes makes tangents with both the circles. If the distance between the two centre of the circles is 8

Since both centers are on the red line y = x,
we can let the smaller circle have radius r and center A(r,r)
and let the larger circle have radius R and center B(R,R) 

We want to find the difference between between R and r,

so we want to find R-r.

We use the distance formula to find the distance between
the centers A(r,r) and B(R,R)

d =   

where (x1,y1) = (r,r)
and where (x2,y2) = (R,R)

We are given that the distance between centers is 8.  
So we have

 = 8
 = 8
 = 8

Divide both sides by 

R-r =  
R-r = 
R-r = 

Edwin