Compare the distance d from the point to the center against the radius r — d < r is inside, d = r is on the circle, d > r is outside.
Module goal. Use one unifying key — comparing a distance against the radius — to judge how a point, a line, and two circles sit relative to one another.
eastmath.com · 18.4 Point, Line, Circle — Who Touches Whom · 18.4.1 Point and Circle: Inside, On, or Outside