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MATH / Three concentric circles are shown. The two largest circles have radii of 12 and 13. If the area of the ring between the two largest circles equals the area of the smallest circle,…

Problem

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

problem

Three concentric circles are shown. The two largest circles have radii of 1212 and 13.13. If the area of the ring between the two largest circles equals the area of the smallest circle, determine the radius of the smallest circle. [asy] import graph; filldraw(circle((0,0),12), lightgray, black+linewidth(1)); filldraw(circle((0,0),10), white, black+linewidth(1)); filldraw(circle((0,0),6), gray, black+linewidth(1)); dot((0,0)); [/asy]
Plain-text mathematical notation (without MathML)
Three concentric circles are shown. The two largest circles have radii of 12 and 13. If the area of the ring between the two largest circles equals the area of the smallest circle, determine the radius of the smallest circle.

[asy]
import graph;
filldraw(circle((0,0),12), lightgray, black+linewidth(1));
filldraw(circle((0,0),10), white, black+linewidth(1));
filldraw(circle((0,0),6), gray, black+linewidth(1));
dot((0,0));
[/asy]
Original LaTeX notation
Three concentric circles are shown. The two largest circles have radii of $12$ and $13.$ If the area of the ring between the two largest circles equals the area of the smallest circle, determine the radius of the smallest circle.

[asy]
import graph;
filldraw(circle((0,0),12), lightgray, black+linewidth(1));
filldraw(circle((0,0),10), white, black+linewidth(1));
filldraw(circle((0,0),6), gray, black+linewidth(1));
dot((0,0));
[/asy]

level

Level 4

type

Prealgebra

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Source and history

task_id
e1f6f5a5-644c-5137-9a8c-f60a0118703a
task_key
prealgebra--test--e1f6f5a5-644c-5137-9a8c-f60a0118703a
task_revision_id
1
config / split
prealgebra / test

Official source

initial import