Hello, rukkk!
Welcome aboard! Code:
C
* * *
* |8 *
A* - - - + - - - *B
* * |D * *
* | *R
* * | * *
* * *
* O *
* *
* *
* *
* * *
We have a circle with center $\displaystyle O.$
The radius is: .$\displaystyle OA = OB = OC = R$
Chord $\displaystyle AB = 64\quad\Rightarrow\quad DB = 32$
Since $\displaystyle CD = 8$, then $\displaystyle DO = R-8$
In right triangle $\displaystyle BDO\!:\;\;DO^2 + DB^2 \:=\:BO^2 \quad\Rightarrow\quad (R-8)^2 + 32^2 \:=\:R^2$
. . $\displaystyle R^2 - 16R + 64 + 1024 \:=\:R^2\quad\Rightarrow\quad 16R \:=\:1088\quad\Rightarrow\quad\boxed{ R \:=\:68}$