A triangle $A B C$ has a fixed base $B C$. If $A B : A C = 1 : 2$, then the locus of the vertex $A$ is\\
(a) a circle whose centre is the midpoint of $B C$.\\
(b) a circle whose centre is on the line $B C$ but not the midpoint of $B C$.\\
(c) a straight line.\\
(d) none of the above.