如图,$AB$是$odotO$的弦,$AB=8,P$是$odotO$上一点(不与点$A,B$重合),过点$O$作$OCperpAP$于点$C$,$ODperpPB$于点$D$,则$CD$的长为<ImageHere>
$becauseOCperpAP,ODperpPB$,$therefore$由垂径定理,得$AC=PC,PD=BD$,$thereforeCD$是$trianglePAB$的中位线,$thereforeCD=frac{1}{2}AB=frac{1}{2}times8=4$.