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设圆\(C:(x-1{)}^{2}+{y}^{2}=1\),过原点\(O\)作圆的任意弦,求所作弦的中点的轨迹方程.
参考答案:\({(x-\frac {1} {2}{)}^{2}}+{{y}^{2}}=\frac {1} {4}(0<x\leqslant 1)\)
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