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.

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