A triangle has an incircle of radius 5.

If two identical circles are placed within the triangle such that they are both tangent to the base, tangent to each other and each tangent to one of the other sides of the triangle, those circles have a radius of 4.

If seven identical circles are placed on the base of the triangle, all tangent to one another in a chain, and the first and last circles tangent to the other sides of the triangle, what is the radius of those circles?

As a bonus question, how many circles of radius 1 can you fit in a tangent chain along the baseline within the triangle?