Question 1045169
What line contains the two points?  What line is perpendicular and contains their midpoint?  The center of the circle is on the intersection of these two lines.



{{{(3-0)/(5-2)}}}
{{{3/3}}}
{{{1}}}
You want line with slope -1 containing  {{{system(x=(5+2)/2=3/2, y=(3+0)/2=3/2)}}}, or the point  ( 3/2, 3/2 ).
Line containing the center is  {{{y-3/2=-1(x-3/2)}}}
{{{y-3/2=-x+3/2}}}
{{{y=-x+6/2}}}
{{{highlight_green(y=-x+3)}}}



Diameter of 6 means RADIUS of 3.
Put this description in the form of the DISTANCE FORMULA:
The distance from  (x, -x+3 ) to (5,3)  must be 3;
and distance from (x, -x+3) to (2,0) must also be 3.