Question 39
Let $O$ be the circum-center of a triangle $ABC$. When points $D$ and $E$ were chosen on the line segments $AB$ and $AC$, respectively, the mid-point of the line segment $DE$ coincided with the point $O$. If $AD = 8$, $BD = 3$ and $AO = 7$, determine the value of $CE$. Here for a line segment $XY$ we denote also by $XY$ its length.