Question 990592
Let centre be (x,y) and radius be r
Now ,
{{{(x-3)^2 + (y-2)^2 = r^2 }}} ---------(i)
{{{(x-5)^2 + (y-3)^2 = r^2 }}} ---------(ii)
{{{(x-2)^2 + (y-5)^2 = r^2 }}} ---------(iii)
Subtracting (ii) from (i), we get,
{{{4x + 2y - 21 = 0}}}---------------------(iv)
Subtracting (iii) from (i), we get,
{{{-2x + 6y - 16 = 0}}} --------------------(v)
Solving  (iv) and (v), we get,
 x = 47/14
 y = 53/14

Put it in any equation to get equation of circle.
(book by S.L.Loney)