The area enclosed within the curve $$\left| x \right| + \left| y \right| = 1$$ is .................

Find the equations of the circle passing through (- 4, 3) and touching the lines x + y = 2 and x - y = 2.

Let A be the centre of the circle $${x^2}\, + \,{y^2}\, - \,2x\,\, - 4y\, - 20 = 0\,$$. Suppose that the tangents at the points B (1, 7) and D (4. - 2) on the circle meet at the point C. Find the area of the quadrilateral ABCD.

Each of the four inequalties given below defines a region in the $$xy$$ plane. One of these four regions does not have the following property. For any two points $$\left( {{x_1},{y_1}} \right)$$ and $$\left( {{x_2},{y_2}} \right)$$ in the region, the point $$\left( {{{{x_1} + {x_2}} \over 2},{{{y_1} + {y_2}} \over 2}} \right)$$ is also in the region. The inequality defining this region is