1.1. In this question all lengths are in centimetres.

The diagram shows the figure $ABC$. The arc $AB$ is part of a circle, centre $O$, radius $r$, and is of length $1.45r$. The point $O$ lies on the straight line $CB$ such that $CO=0.5r$.

Find, in radians, the angle $AOB$.

1.2. Find the area of $ABC$, giving your  in the form $k{r}^{2}$, where $k$ is a constant.

1.3. Given that the perimeter of $ABC$ is $12cm$, find the value of $r$.