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Using the conditions $r > \frac{3}{2}$ and $\theta < \frac{3}{4}$, work out the values of $r$ and $\theta$.
Mathematics 9709 · AS & A Level · Circular measure
Circular measure — practice question
The diagram depicts a metal plate $OABCDE$ made up of sectors from two circles, both with centre $O$. The radii of sectors $AOB$ and $EOF$ are $r$ cm, while sector $COD$ has radius $2r$ cm. The angle $AOB = \text{angle } EOF = \theta$ radians and the angle $COD = 2\theta$ radians. It is given that the plate has perimeter $14$ cm and area $10\text{ cm}^2$.