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(B) The equation of the circle is $x^{2} + y^{2} - 4x + 3 = 0$,which can be written as $(x-2)^{2} + y^{2} = 1$. The center is $C(2,0)$ and radius $r =

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$\frac{3\sqrt{3}}{4}$

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(B) The equation of the circle is $x^{2} + y^{2} - 4x + 3 = 0$,which can be written as $(x-2)^{2} + y^{2} = 1$. The center is $C(2,0)$ and radius $r = 1$.Since the tangents from the origin $O(0,0)$ meet the circle at $A$ and $B$,the chord of contact $AB$ is given by $T = 0$.For the circle $x^{2} + y^{2} - 4x + 3 = 0$,the chord of contact from $(0,0)$ is $0(x) + 0(y) - 2(x+0) + 3 = 0$,which simplifies to $2x = 3$ or $x = \frac{3}{2}$.The distance from the center $C(2,0)$ to the chord $AB$ is $d = |2 - \frac{3}{2}| = \frac{1}{2}$.The length of the chord $AB$ is $2\sqrt{r^{2} - d^{2}} = 2\sqrt{1^{2} - (\frac{1}{2})^{2}} = 2\sqrt{\frac{3}{4}} = \sqrt{3}$.In $	riangle OAB$,the base is $AB = \sqrt{3}$ and the height $OM$ is the distance from the origin to the line $x = \frac{3}{2}$,which is $\frac{3}{2}$.Area of $	riangle OAB = \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height} = \frac{1}{2} 	imes \sqrt{3} 	imes \frac{3}{2} = \frac{3\sqrt{3}}{4}$.

Let the tangents at two points $A$ and $B$ on the circle $x^{2} + y^{2} - 4x + 3 = 0$ meet at the origin $O(0,0)$. Then the area of the triangle $OAB$ is:

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