摘要： 解:(1)如图所示:······························································································ 4分 (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为直径的圆． 8分 (3)此中转站应建在的外接圆圆心处(线段的垂直平分线与线段的垂直平分线的交点处)． 10分 理由如下: 由. .. 故是锐角三角形. 所以其最小覆盖圆为的外接圆. 设此外接圆为.直线与交于点. 则． 故点在内.从而也是四边形的最小覆盖圆． 所以中转站建在的外接圆圆心处.能够符合题中要求． ························································································ 12分

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