Problem

The diagram shows a metal plate $OABCDEF$ consisting of sectors of two circles, each with centre $O$. The radii of sectors $AOB$ and $EOF$ are $r$ cm and the radius of sector $COD$ is $2r$ cm. Angle $AOB=$ angle $EOF=\theta$ radians and angle $COD=2\theta$ radians.

It is given that the perimeter of the plate is $14$ cm and the area of the plate is $10\text{ cm}^2$.

Given that $r>\dfrac{3}{2}$ and $\theta<\dfrac{3}{4}$, find the values of $r$ and $\theta$.