Question 158
The plan of a castle is made as follows: consider a circle of length $2019$ metres with an inscribed regular polygon with $2019$ vertices. After numbering the vertices of the polygon from $1$ to $2019$ clockwise, draw circles of length $2019$ m centred at every point whose number is a perfect square. The plan of the castle consists of the union of all the discs drawn. How many metres does the perimeter of the castle measure?
(A) 2692
(B) 4038
(C) 4627
(D) $\frac{29370}{2 \pi}$
(E) $2019 \pi$
(A) 2692
(B) 4038
(C) 4627
(D) $\frac{29370}{2 \pi}$
(E) $2019 \pi$