If a tower subtends equal angles at four points P, Q, R and S that...

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

so,~$PF = hcot \theta$,

similarly,~$QF = RF = SF = hcot \theta$
$⇒$ points~$P, Q, R, S$ lie on the same circle
$⇒$ 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