Filling the holes - Colegiul National C. Negruzzi (Iași - Roumanie)

(a) There is a triangle that has side L with three tangent circles inside.Determine the radius of the circles that can be drawn in each of the regions within the triangle that are not covered by the three circles.
(b) Same requirement for side square L with four tangent circles inside.
(c) What is the smallest regular tetrahedron that can contain four radius balls?
(d) What is the radius of the largest ball that fits within the space between the three balls?