Hello, Beggarsbelief!
Code:

 * * *
* *
*  *
*  *

Q*  A *
* o *  o *
* *  * *
*  *
* * oM * *
 *
* * * *
*o+*o*
* B  *P

*  *
*  *
*  *
* * * 

The centers of the circles are and
The circles intersect at and
Draw chord
Draw segment
It can be shown that they intersect at
Code:
Q 
o 
*  A
*  o
*  * :
*  * :2
4 *M * :
+      o      +
: * * 4
2: *  *
: * 4 *
o  *
B  *
+o
 2 P

Note that: . . . . Quadrilateral is a rhombus.
We are told that: .
. . .We find that: . . . . is a square.
To go from from to , we go left 2, up 4.
. . Then, to go from to , we got right 4, up 2.
. . Hence, center is at
. . To go from to , we go left 4, down 2.
. . Hence, center is at
Now you can write the equations of the circles.