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MATH / Each of the small circles in the figure has radius one. The innermost circle is…

Problem

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

problem

Each of the small circles in the figure has radius one. The innermost circle is tangent to the six circles that surround it, and each of those circles is tangent to the large circle and to its small-circle neighbors. Find the area of the shaded region.

[asy]
fill(Circle((0,0),3),gray(0.7));
fill(Circle((0,0),1),white);
fill(Circle((1.73,1),1),white);
fill(Circle((-1.73,1),1),white);
fill(Circle((-1.73,-1),1),white);
fill(Circle((1.73,-1),1),white);
fill(Circle((0,2),1),white);
fill(Circle((0,-2),1),white);
[/asy]

level

Level 2

type

Geometry

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Source and history

task_id
95a389df-6199-53f6-a260-498dfb8cefe2
task_key
geometry--test--95a389df-6199-53f6-a260-498dfb8cefe2
task_revision_id
1
config / split
geometry / test

Official source

initial import