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(C) The given equation of the circle is $x^2+y^2=4$. On differentiating with respect to $x$,we get $2x + 2y \frac{dy}{dx} = 0$,which implies $\frac{dy

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$2 \sqrt{3}$

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(C) The given equation of the circle is $x^2+y^2=4$. On differentiating with respect to $x$,we get $2x + 2y \frac{dy}{dx} = 0$,which implies $\frac{dy}{dx} = -\frac{x}{y}$. At the point $(1, \sqrt{3})$,the slope of the tangent is $m_t = -\frac{1}{\sqrt{3}}$. The equation of the tangent at $(1, \sqrt{3})$ is $y - \sqrt{3} = -\frac{1}{\sqrt{3}}(x - 1)$,which simplifies to $x + \sqrt{3}y = 4$. This tangent intersects the $x$-axis at point $B(4, 0)$. The slope of the normal at $(1, \sqrt{3})$ is $m_n = -\frac{1}{m_t} = \sqrt{3}$. The equation of the normal at $(1, \sqrt{3})$ is $y - \sqrt{3} = \sqrt{3}(x - 1)$,which simplifies to $y = \sqrt{3}x$. This normal passes through the origin $O(0, 0)$. The triangle formed by the positive $x$-axis,the tangent,and the normal is $	riangle OAB$,where $O(0, 0)$,$A(1, \sqrt{3})$,and $B(4, 0)$. The area of $	riangle OAB$ is given by $\frac{1}{2} 	imes 	ext{base} 	imes 	ext{height} = \frac{1}{2} 	imes OB 	imes AD$,where $AD$ is the $y$-coordinate of point $A$. Area $\Delta = \frac{1}{2} 	imes 4 	imes \sqrt{3} = 2\sqrt{3}$.

If $\Delta$ is the area of the triangle formed by the positive $x$-axis and the normal and tangent to the circle $x^2+y^2=4$ at $(1, \sqrt{3})$,then $\Delta$ is equal to

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