中考数学压轴题详解—圆(7)

复习圆

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 MNOM 31

6 2

∠MON 30

又cos∠

MON

ON

OM

ON OM cos30 在Rt△OCN中

OC ON

cos30 9

2

CN ON sin30 12

2

N的坐标为 9 2， 2 ··································································································· 3分

（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

9

2x k 直线ON

的解析式为y 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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