2014中考数学专题复习 - 压轴题（含答案）

（注：正确画出1个图得2分，无作图痕迹或痕迹不正确不得分） （2）若三角形为锐角三角形，则其最小覆盖圆为其外接圆； ·································· 6分

若三角形为直角或钝角三角形，则其最小覆盖圆是以三角形最长边（直角或钝角所对的边）为直径的圆． ·················································································································· 8分

（3）此中转站应建在△EFH的外接圆圆心处（线段EF的垂直平分线与线段EH的垂直平分线的交点处）． ·········································································· 10分 理由如下：

由?HEF??HEG??GEF?47.8??35.1??82.9?，

?EHF?50.0?，?EFH?47.1?，

故△EFH是锐角三角形，

所以其最小覆盖圆为△EFH的外接圆，

设此外接圆为?O，直线EG与?O交于点E，M， 则?EMF??EHF?50.0??53.8???EGF．

故点G在?O内，从而?O也是四边形EFGH的最小覆盖圆．所以中转站建在△EFH的外接圆圆心处，能够符合题中要求． ············································································ 12分

G M H 32.4? 49.8?53.8 ? 50.0? 44.0? 47.1? F

47.8?35.1 ? E