1973 AMC 12 Question 30 - thichhoctoan.com

Question 30

Let $[t]$ denote the greatest integer not exceeding $t,$ where $t\ge0,$ and $$
\begin{aligned} S=\{(x,y):{}&(x-T)^2+y^2\\ &\le T^2\},\\ T&=t-[t]. \end{aligned}
$$ Then we have

the point $(0,0)$ does not belong to $S$ for any $t$
$0\le\operatorname{Area} S\le\pi$ for all
$t$
$S$ is contained in the first quadrant for all $t\ge5$
the center of $S$ for any $t$ is on the line $y=x$
none of the other statements is true