The x-coordinate of the center of the circle in the first quadrant ...

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The x-coordinate of the center of the circle in the first quadrant (see figure) tangent to the lines \( \mathrm{y}=\frac{1}{2} \mathrm{x}, \mathrm{y}=4 \) and the \( \mathrm{x} \)-axis is
(A) \( 4+2 \sqrt{5} \)
(B) \( 4+\frac{8 \sqrt{5}}{5} \)
\( -(\mathrm{C}) 2+\frac{6 \sqrt{5}}{5} \)
P
W
(D) \( 8+2 \sqrt{5} \)
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