Question 54
$\triangle ABC$ has area $1$ and satisfies $AB \gt AC$. The internal bisector of $\angle A$ meets $BC$ at $D$, and $\triangle DBC'$ is similar to $\triangle ABC$ where $C'$ is the image of $C$ upon reflection across $AD$. When the perimeter of $\triangle ABC$ is minimised, find the length of $AB$.