A straight line x = y + 2 touches the circle 4(x² + y²) = r². The value of r is

If the centre of the circle passing through the origin is (3, 4), then the intercepts cut-off by the circle on X-axis and Y-axis respectively, are

What is the radius of the circle passing through the point (2, 4) and having centre at the intersection of the lines x $$-$$ y = 4 and 2x + 3y + 7 = 0 ?

Consider the two circles $${(x - 1)^2} + {(y - 3)^2} = {r^2}$$ and $${x^2} + {y^2} - 8x + 2y + 8 = 0$$

What is the distance between the centres of the two circles?