Two unit circles are completely enclosed by a
ring of four identical circles. Find the minimum radius of the surrounding circles.
Note: A ring of circles is a set where each is externally tangent to exactly two others and they enclose a single region.
With two of the ring circles situated side by side, a small circle of radius r is nestled between them such that the top of their circumferences our co-linear.
If we draw a triangle between a ring circle center, the two ring circles' tangent point
and the center of the small circle,
we see this is a (1-r, 1, 1+r) right triangle.
(1-r)^2 + 1^2 = (1+r)^2
r=1/4
Edited on August 30, 2024, 10:50 am
soln