Three points not all on one line can be circled by exactly one circle and no other — this is a triangle's circumscribed circle.
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 · 18.4.4 How Many Points Fix a Circle