If a tower subtends equal angles at four points P , Q , R and S that lie in a plane containing the foot of the tower, then which of the following statements is always true (here, the tower is perpendicular to the plane containing the points P , Q , R , S )

Step-by-step solution

Let, top of the tower is T , foot of the tower is F, height of the tower is h & ∠ T P F = θ Because T P F is a right-angled Δ so, P F = h cot ⁡ θ , similarly, Q F = R F = S F = h cot ⁡ θ ⇒ 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 C is always correct