非选择题。读“南水北调中线一期工程路线示意图”与相关气候资料图，回答下列问题。

已知圆C的方程为：x²+y²﹣2x﹣4y+m=0．

（1）求m的取值范围；

（2）若圆C与直线3x+4y﹣6=0交于M、N两点，且|MN|=2$\sqrt{3}$，求m的值；

（3）设直线x﹣y﹣1=0与圆C交于A、B两点，是否存在实数m，使得以AB为直径的圆过原点，若存在，求出实数m的值；若不存在，请说明理由．

a (x-2a) +a(2a-x)  =____.

阅读下面的短文，从每题所给的A、B、C三个选项中选出最佳答案。

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