中考数学压轴题详解—圆1(7)

7 解：（1）解方程x2 12x 27 0，得x1 9，x2 3

A在B的左侧

OA 3，OB 9 AB OB OA 6

OM的直径为6········································································································· 1分

（2）过N作NC⊥OM，垂足为C， 连结MN，则MN⊥ON

sin∠MON

MN31OM

6

2

∠MON 30

又cos∠

MON

ONOM

ON OM cos30

在Rt△OCN中

OC ON

cos30

2

92

CN ON sin30

1

2

2

N的坐标为 9 ，

··························································································· 3分 22

（用其它方法求N的坐标，只要方法合理，结论正确，均可给分．） 设直线ON的解析式为y

kx

9x k 2

2

3

直线ON

的解析式为y

3

x·

··············································································· 4分 （3）如图2，T1，T2，T3，T4为所求作的点，△OT1N，△OT2N，△OT3N，△OT4N为所求等腰三角形．（每作出一种图形给一分） ·································································································· 8分

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