AMC 8 2018 Problem 15

In the diagram below, a diameter of each of the two smaller circles is a radius of the larger circle. If the two smaller circles have a combined area of $1$ square unit, then what is the area of the shaded region, in square units?

$\textbf{(A) } \frac{1}{4} \textbf{(B) } \frac{1}{3} \textbf{(C) } \frac{1}{2} \textbf{(D) } 1 \textbf{(E) } \frac{\pi}{2}$