Rectangle ABCD is inscribed in circle P. What is the area of circle P?

(1) The area of rectangle ABCD is 100.

(2) Rectangle ABCD is a square.


I said A because if a rectangle ABCD is inscribed in a circle, it must be a square. If it is a square, it's side must be 10, and it's diagonal 10(root2). Therefore, we can calculate the area of the circle.

However, official answer says C.

Why is my reasoning incorrect?