



 
This is the diagram Kevin sent Hi Kevin, I redrew your diagram because I want to add to it. The sectors $ABC$ and $DFC$ are similar and hence 29.8 is to 21.4 as $BC$ is to $FC,$ that is \[\frac{29.8}{21.4}= \frac{r + 14.5}{r}\] Solve for $r.$ If $a$ is the length of an arc of a circle or radius $r$ and the arc is subtended by the angle with measure $\theta$ radians than $a = r \times \theta.$ Hence using the arc $DF$ which is subtended by the angle $FCD$ we get \[21.4 = r \times \theta,\] where $\theta$ is the measure of the angle $FCD$ in radians. You know $r$ and hence you can solve for $\theta.$ The angle $CF$ is a right angle and and the measure of the angle $FCE$ is $\large \frac{\theta}{2}.$ Hence \[\cos \frac{\theta}{2} = \frac{h}{r}.\] This allows you to solve for $h$ and $x = r  h.$ (When using your calculator to calculate $\cos \frac{\theta}{2}$ make sure you have it set on radians and not degrees.) Write back if you need more assistance,  


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