Enjoy the Fourth of July – America’s 250th birthday
[1]
A 30° – 60° – 90° triangle is packed with an infinite number of circles. Due to time constraints, only a few circles are drawn, although they are infinite.
The circles are tangent to adjacent circles and to the triangle at the three vertices.
The largest circle has an area of 1776 square centimeters.
Assume an infinite progression of the circles, in all three directions.
Find the area of the purple region.
A correct answer sent to [email protected] [2] may win a Tucker’s gift card.
Last week’s winner [3] was Tim Stacho with Area = 1215 square centimeters.
(Use of AI is strictly prohibited.)
Jeff Smith is a former Math teacher and a retired US Navy Lieutenant Commander. Reach him at [email protected] [2].