$$|\mathrm{OM}| = 2 \text{ units}$$
In the rectangular coordinate plane, a semicircle with center at point M and a quarter circle with center at the origin intersect at point A as shown in the figure.
Accordingly, what is the x-coordinate of point A?
A) $\frac{5}{3}$
B) $\sqrt{2}$
C) $\frac{\sqrt{3}}{2}$
D) $\frac{3}{2}$
E) $\sqrt{3}$