# 4 circles

• Jul 24th 2009, 05:09 AM
Wilmer
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.
• Jul 24th 2009, 01:07 PM
aidan
Quote:

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
• Jul 24th 2009, 05:17 PM
Wilmer
Quote:

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.
• Jul 26th 2009, 10:15 AM
Wilmer
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?!