Suppose that there are four points $A, B, C, D$. A circle of radius $r_A$ surrounds point $A$, a circle of radius $r_C$ surrounds point $C$, and a circle of radius $|DB|$ surrounds point $D$. $AB||BC$, $|AB|=|BC|$. Circle $D$ intersects circles $A$ and $C$ exactly once per circle, at different points, in addition to intersecting with point $B$.
How to solve $|DB|$ algebraically (preferably without iterating) knowing only the values of $r_A$, $r_C$ and $|AB|$?