OACB is a parallelogram. In other words if $\left \|\mathbf{a}+k\mathbf{b} \right \|=1$ ($k\in\mathbb{R}$), prove that
$\|\mathbf{a}\| \cdot \|\mathbf{b} \| \cdot \sin \theta \leq \|\mathbf{b} \| $ where $\theta$ is the angle of the two vectors.
Any suggestion?