Question is: Find the length of $\text{AO}$ and $\text{BO}$
My work, with the things I know already:
- Length: $\text{CO}=r$ and $\text{TO}=\frac{r}{4}$ and $\text{TG}=\frac{r}{2}$ and $\text{CT}=\frac{r\sqrt{17}}{4}$ and $\text{DG}=r\sqrt{\frac{17+\sqrt{17}}{34}}$
- Length: $\text{KG}=r\sqrt{\frac{1}{2}-\frac{1}{2\sqrt{17}}}$ and $\text{TH}=\frac{r}{4}\sqrt{5-2\sqrt{2-\frac{2}{\sqrt{17}}}}$
- Length: $\text{FT}=\frac{r}{4}\sqrt{5-\sqrt{8+\frac{8}{\sqrt{17}}}}$ and $\text{HG}=\text{GF}=\frac{r}{4}$ and $\text{DK}=\frac{r}{2}$
- Angle: $\theta_9+\theta_{10}=\frac{\pi}{2}$ and $\theta_1=\arctan\left(\frac{1}{4}\right)$ and $\theta_7+\theta_{11}=\frac{\pi}{2}+\arctan\left(\frac{1}{4}\right)$
