A circle, $C_1$, has equation $x^2 + y^2 - 4x + 6y = 36$.

1. Rearrange the equation by completing the square for $x$ and $y$ terms

$x^2 - 4x + y^2 + 6y = 36$
$(x - 2)^2 - 2^2 + (y + 3)^2 - 3^2 = 36$
$(x - 2)^2 - 4 + (y + 3)^2 - 9 = 36$
$(x - 2)^2 + (y + 3)^2 = 49$

2. Identify the coordinates of the centre

Comparing with $(x - a)^2 + (y - b)^2 = r^2$, the centre $(a, b)$ is $(2, -3)$.

3. Calculate the radius

$r^2 = 49$
$r = \sqrt{49} = 7$