We have the equations of these three circles
(x - 2)^2 + ( y - 3)^2 = 9 ⇒ (y - 3)^2 = 9 - (x - 2)^2 (1)
(x + 5)^2 + (y - 3)^2 = 16 (2)
(x + 1)^2 + ( x + 2)^2 = 25
Sub (1) into (2) for (y - 3)^2.....and we have that
( x + 5)^2 + 9 - (x - 2)^2 = 16 simplify
x^2 + 10x + 25 + 9 - x^2 + 4x - 4 = 16
14x + 30 = 16
14x = - 14
x = -1 this is the x coordinate of the epicenter
Use (1) to find the y coordinate of the epicenter
( y - 3)^2 = 9 - (-1 - 2)^2
(y - 3)^2 = 9 - 9
(y - 3)^2 = 0 take the square root
y - 3 = 0
y = 3
The epicenter is (-1,3)
This graph shows the situation : https://www.desmos.com/calculator/6ofwemeyej
