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