Review Example 2 under "Reflection".  For 2.15, to minimize sum of the segments, you want to reflect them so that the straight line can be drawn.

For 2.16, reflect the point $P$ across the center $O$ to point $P'$, then $CP^2+DP^2 = CP^2+CP'^2$. Then find out about the relation among $CP$, $CP'$, $OC$, and $OP$.