If the area of the triangle formed by the positive x-axis, the normal and the tangent to the circle (x $$-$$ 2)² + (y $$-$$ 3)² = 25 at the point (5, 7) is A, then 24A is equal to _________.

If one of the diameters of the circle x² + y² - 2x - 6y + 6 = 0 is a chord of another circle 'C', whose center is at (2, 1), then its radius is ________.

Let PQ be a diameter of the circle x² + y² = 9. If $$\alpha $$ and $$\beta $$ are the lengths of the perpendiculars from P and Q on the straight line,
x + y = 2 respectively, then the maximum value of $$\alpha\beta $$ is _____.

The diameter of the circle, whose centre lies on the line x + y = 2 in the first quadrant and which touches both the lines x = 3 and y = 2, is _______ .