Let, top of the tower is $T$, foot of the tower is $\mathrm{F,}$ height of the tower is $h$ & $\mathrm{\angle }TPF=\theta$
Because $TPF$ is a right-angled $\mathrm{\Delta }$

so, $PF=h\cot \theta$,

similarly, $QF=RF=SF=h\cot \theta$
$\Rightarrow$ points $P,Q,R,S$ lie on the same circle
$\Rightarrow$ points $P,Q,R,S$ are vertices of a cyclic quadrilateral but may or may not be consecutive vertices in the same order
Hence, options $A,B$ & $D$ may or may not be correct.
But, option $\left(C\right)$ is always correct