Tangent Circles / Spheres
I love this type of problems since they really challenge our visualization ability. Most of the time, we can use the properties of tangent circles to turn 3D problems into 2D (by "cutting" along an appropriate plane) and / or turn 2D circle problems into 2D triangle / line segment problems (by connecting centers and tangent points)
2022 AIME II Problem 3 Problem 7