1. ## 4 circles

Ready to run around in circles?

Four circles radius 4, centers (4,9), (28,9), (16,4), (16,18),
are each tangent to one side of an isosceles trapezoid.
All four tangent points are situated at middle of each side.

Gimme the trapezoid's side lengths (the one with height=6).

If you wish, you could try the possible trapezoid(s) that contain
the four circles.

2. Originally Posted by Wilmer
Ready to run around in circles?

Four circles radius 4, centers (4,9), (28,9), (16,4), (16,18),
are each tangent to one side of an isosceles trapezoid.
All four tangent points are situated at middle of each side.

Gimme the trapezoid's side lengths (the one with height=6).

If you wish, you could try the possible trapezoid(s) that contain
the four circles.
h = 6, side dim = 6.93

3. Originally Posted by aidan
h = 6, side dim = 6.93
Agree. Your C2 diagram: equal sides = 12 / sqrt(3) ; your 6.93.
Other 2 sides: 24 - 6sqrt(3) and 24 -2 sqrt(3).

NICE diagrams. Thanks.

4. ## General case

Four circles radius 4, centers (4,9), (28,9), (16,4), (16,18) : original givens

Four circles radius r, centers (r,w), (3r+2u,w), (2r+u,r), (2r+u,3r+2v) : as a general case

General case where all 4 circles are outside the trapezoid
===========================================

4 circles radius r, centers (r,w), (3r+2u,w), (2r+u,r), (2r+u,3r+2v)

longer parallel side = 2(2r + u - b)
shorter parallel side = 2[2(r - a) + u + b]
the two equal sides = 2SQRT[(a - b)^2 + v^2]

where
a = r + sqrt(r^2 - k) where k = 4r(r + v - w) + (v - w)^2
b = [v(2r + v - w) + a(r - a)] / (r - a)

Anybody disagree?!