If a circle touches both axes in the first quadrant, its centre is at (r,r) and radius is r. Distance from centre (r,r) to the line x−y−2=0 must equal the radius r : ‌
|r−r−2|
√12+(−1)2
=r ‌
|−2|
√2
=r ‌
2
√2
=r⇒r=√2 Area of the circle: πr2=π(√2)2=2π.