yomikoma

I did some trig. If the radius of each small circle is 1, then the radius of the next larger circles solves r^2 - 2( 1 / cos 36 + tan^2 36 ) r + 1 = 0, or approximately r=3.2170. If the center of the small pentagon of circles is the origin, then the coordinates of the center of the small circle above the origin is (0, 1/tan 36) = (0, 1.3764). The center of the medium circle above and to the right is (r, r/tan 36) = (3.2170, 4.4278). The other centers are rotated by an angle of 72 degrees about the origin.