95. Let $O$ be the center of the circle, $C$ a point on the circle, and $M$ the midpoint of $OC$. $A$ and $B$ are points on the circle such that $\widehat{A M O}=\widehat{B M C}$; $A$ and $B$ lie on the same side of the line $O C$. Find $|A B|$, if $|A M| - |B M| = a$.
95. Note that points $A, O, M, B$ lie on the same circle ( $\widehat{A M B}$ is measured as the half-sum of arc $\widehat{A B}$ and the arc symmetric to $\breve{A B}$ with respect to $O C$, i.e., $\widehat{A M B}=\widehat{A O B}$ ). Further, let $|M K|=|M B|$ on $A M$, then $\triangle A K B$ is similar to $\triangle O M B$.

Answer: $|A B|=2 a$.