Solution of the Week #511 - Seven Circles

They will have a radius of 2. The base of the triangle will be 40, but the other sides cannot be determined.

17 circles of radius 1 will fit along the baseline.

 In general I have found that if one circle has radius A and two circles have radius B, then n circles will have radius:

 r_n = AB/((n-1)A-(n-2)B)

 In our case A=5, B=4. When n=7, r_7 = 20/(30-20) = 2.

 Reverse engineering r_n = 1:

 1 = 20/(5(n-1)-4(n-2)) = 20/(n-5+8)

20 = n-5+8

n = 17