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MATH / Four circles of radius 1 are each tangent to two sides of a square and…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Four circles of radius 1 are each tangent to two sides of a square and externally tangent to a circle of radius 2, as shown.  What is the area of the square?

[asy]
unitsize(1cm);draw(Circle((0,0),2));
for(int i=0; i<4; ++i) {
	draw(Circle(scale(3)*dir(45+90*i),1));
	draw((3+sqrt(2))*dir(45+90*i)--(3+sqrt(2))*dir(-45+90*i));  
}
draw((0,0)--(2,0));
label("2",(1,0),N);
draw(scale(3)*dir(45+90*1)--shift((1,0))*scale(3)*dir(45+90*1));
label("1",point(scale(3)*dir(45+90*1)--shift((1,0))*scale(3)*dir(45+90*1),.5),S);
[/asy]

level

Level 5

type

Geometry

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Source and history

task_id
4e069a28-a5d3-5528-be4f-faf1667bfe5f
task_key
geometry--test--4e069a28-a5d3-5528-be4f-faf1667bfe5f
task_revision_id
1
config / split
geometry / test

Official source

initial import