Had "fun" with this:
Circle radius 65 has center M(65,65), thus tangent to both x and y positive axis.
ABCD is a cyclic quad, it's vertices on the circumference of circle M.
It's area is 6072 square units.
Coordinates of A are (2,81), coordinates of C are (98,9).
What are the coordinates of B and D?
In case some of you suspect I'm "fishing" for an answer:
the x and y coordinates of B and D add up to 260 (that's from my solution).
I'm posting this for your pleasure(!), hoping nobody finds more than 1 solution