I went halfway, than I got stuck.

Question:Find the cord AB

I drew in my own line, OC and found the length of that, than I found the length of PB

$\displaystyle 8sin65=OC$

$\displaystyle OC=7.254046...$

$\displaystyle 8cos65=PC$

PC=3,380944...

$\displaystyle cos^-1(OC/11)=O$

$\displaystyle O=49.741394...

$

$\displaystyle 11sin49.741394=BC$

$\displaystyle BC=8.26914843$

Now how do I find the segment AP?