Step-by-Step Solution
Key Concept: Points equidistant from the foot of a tower and subtending equal angles to the top form vertices of a cyclic quadrilateral
Let $T$ be the top of the tower and $F$ be the foot of the tower with height $h$. Since $\angle TPF = \theta$ is a right-angled triangle, we have $PF = h\cot\theta$. Similarly, $QF = RF = SF = h\cot\theta$, which means points $P, Q, R, S$ all lie on a circle. Since $P, Q, R, S$ are vertices of a cyclic quadrilateral, they may or may not be consecutive vertices in the same order. Therefore, options A, B, and D may or may not be correct, but option C (stating the geometric relationship) is always correct.
Correct Answer: 3