Question

如图，已知□ABCD的对角线AC、BD相交于点O，AC =12，BD=18，且△AOB的周长l=23，求AB的长．

Answer

8

【解析】∵□ABCD的对角线AC、BD相交于点O，AC =12，BD=18，·········· 1分

∴ AO=AC=6，······························· 3分

BO=BD=9．································· 5分

又∵△AOB的周长l=23，∴ AB=l–(AO+BO)=23–(6+9)=8．············· 7分

根据平行四边形中两条对角线相互平分的性质可求解