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

The common chord of the circles $${x^2} + {y^2} - 4x - 4y = 0$$ and $$2{x^2} + 2{y^2} = 32$$ subtends at the origin an angle equal to

The locus of the mid-points of the chords of the circle $${x^2} + {y^2} + 2x - 2y - 2 = 0$$, which make an angle of 90$$^\circ$$ at the centre is

If one of the diameters of the curve x² + y² $$-$$ 4x $$-$$ 6y + 9 = 0 is a chord of a circle with centre (1, 1), the radius of this circle is