\(AC\) is a semicircle and \(ABCD\) is a square. Alex and Brian each began at point \(C\) and traveled to point \(A,\) with Alex taking the route of the semicircle to get there and Brian following the square from point \(C\) to point \(D,\) then from point \(D\) to point \(B,\) then from \(B\) to point \(A.\) If they each departed point \(C\) at the same time and then arrived at point \(A\) at the same time, what is the ratio of Alex's rate to Brian's rate?

A. \(\dfrac{\pi}6\)

B. \(\dfrac{\pi}4\)

C. \(\dfrac{\pi}3\)

D. \(\dfrac{\pi}2\)

E. \(\dfrac{2\pi}3\)

Answer: A

Source: Veritas Prep