Circle tangent to the x-axis

Consider the circle $(x - 2)^2 + (y - 2)^2 = 4$ with center $(2, 2)$ and radius $2$. The distance from the center to the $x$-axis is the center's $y$-coordinate $2$, which equals the radius $2$.

When the distance from the center to a line equals the radius, the circle is tangent to that line. So this circle touches the $x$-axis, at the point directly below the center, $(2, 0)$. In general a circle with center $(a, b)$ and radius $r$ is tangent to the $x$-axis exactly when $|b| = r$. The large dots mark the tangent point $(2, 0)$ and the center $(2, 2)$.