Two circles from a distance

Geometry Level 2

$BC$ is tangent to both a circle with center at $A$ and a circle with center at $D$ . The area of the circle with center at $A$ is $225\pi$ and the area of the circle with center at $D$ is $36\pi$ .

If $BC=16$ , find the distance between the centers of the two circles.

\sqrt{697}

\dfrac{1}{7}\pi+\sqrt{697}

\dfrac{5\sqrt{697}}{7}+\dfrac{2\sqrt{679}}{7}

\sqrt{\dfrac{17425}{49}}+\sqrt{\dfrac{27888}{49}}