Hamilton Mathematical Olympiad 2016 Q6

The diagram shows two arcs. Arc $AB$ is one eighth of a circle with centre $C$, and arc $AC$ is one quarter of a circle with centre $D$. The points $A$ and $B$ are joined by straight lines to $C$, and $A$ and $C$ are joined by straight lines to $D$.

Prove that the area of the shaded triangle $T$ is equal to the area of the shaded region $R$.

Input note: let $DA=r$ and write down the exact value of both areas in terms of $r$.