1. The solution to the equation $\left|\sqrt{(x-2)^{2}}-1\right|=x$ is ).
(A) $\frac{3}{2}$
(B) $\frac{1}{2}$
(C) $\frac{3}{2}$ or $\frac{1}{2}$
(D) No solution
$\begin{array}{l}\text { I. 1. B } \\ \text { 1. Hint: } 0 \leqslant x<2,|1-x|=x, x^{2}-2 x \\ +1=x^{2}, x=\frac{1}{2} .\end{array}$