AT-OEMO-FED1 1991 Problem 4

Let $AB$ be a chord of a circle $k$ of radius $r$ , with $AB=c$ . $(a)$ Construct the triangle $ABC$ with $C$ on $k$ in which a median from $A$ or $B$ is of a given length $d.$ $(b)$ For which $c$ and $d$ is this triangle unique?