Finding Intersection Point of Circle and Line

In a coordinate plane, a circle is centered at the point $(3, -2)$ with a radius of $5$. A line perpendicular to the radius at the point $(3 + 5, -2)$ intersects the circle again at the point $(x, y)$. What are the coordinates of the intersection point?

The equation of a circle in the coordinate plane is given by:

$$ (x - h)^2 + (y - k)^2 = r^2 $$

where $(h, k)$ is the center and $r$ is the radius.