AMC 12 2018b Problem 4

A circle has a chord of length $10$, and the distance from the center of the circle to the chord is $5$. What is the area of the circle?

$\textbf{(A) }25\pi \textbf{(B) }50\pi \textbf{(C) }75\pi \textbf{(D) }100\pi \textbf{(E) }125\pi$