Let the tangent to the circle C_{1} : x^{2} + y^{2} = 2 at the point M($$-$$1, 1) intersect the circle C_{2} : (x $$-$$ 3)^{2} + (y $$-$$ 2)^{2} = 5, at two distinct points A and B. If the tangents to C_{2} at the points A and B intersect at N, then the area of the triangle ANB is equal to :

If the tangents drawn at the points $$O(0,0)$$ and $$P\left( {1 + \sqrt 5 ,2} \right)$$ on the circle $${x^2} + {y^2} - 2x - 4y = 0$$ intersect at the point Q, then the area of the triangle OPQ is equal to :

The set of values of k, for which the circle $$C:4{x^2} + 4{y^2} - 12x + 8y + k = 0$$ lies inside the fourth quadrant and the point $$\left( {1, - {1 \over 3}} \right)$$ lies on or inside the circle C, is :

Let C be a circle passing through the points A(2, $$-$$1) and B(3, 4). The line segment AB s not a diameter of C. If r is the radius of C and its centre lies on the circle $${(x - 5)^2} + {(y - 1)^2} = {{13} \over 2}$$, then r^{2} is equal to :