AHSME 1973 Problem 30

Let $[t]$ denote the greatest integer $\leq t$ where $t \geq 0$ and $S = \{(x,y): (x-T)^2 + y^2 \leq T^2 \text{ where } T = t - [t]\}$. Then we have $\textbf{(A)}\ \text{the point } (0,0) \text{ does not belong to } S \text{ for any } t$ $\textbf{(B)}\ 0 \leq \text{Area } S \leq \pi \text{ for all } t$ $\textbf{(C)}\ S \text{ is contained in the first quadrant for all } t \geq 5$ $\textbf{(D)}\ \text{the center of } S \text{ for any } t \text{ is on the line } y=x$ $\textbf{(E)}\ \text{none of the other statements is true}$