Two tangents to the circle $x^{2}+y^{2}=4$ at the points A and B meet at the point $P(-4,0)$. Then the area of the quadrilateral PAOB, O being the origin, is
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Logic Tip: The length of a tangent $L$ from a point $(x_1, y_1)$ to a circle $x^2 + y^2 = r^2$ is simply $L = \sqrt{x_1^2 + y_1^2 - r^2}$. Here, $L = \sqrt{(-4)^2 + 0 - 4} = \sqrt{12} = 2\sqrt{3}$. The area is immediately $r \times L = 2 \times 2\sqrt{3} = 4\sqrt{3}$.