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MATH / Three circles of radius s are drawn in the first quadrant of the xy-plane. The first circle is tangent to both axes, the second is tangent to the first circle and the x-axis, and t…

Problem

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

problem

Three circles of radius ss are drawn in the first quadrant of the xyxy-plane. The first circle is tangent to both axes, the second is tangent to the first circle and the xx-axis, and the third is tangent to the first circle and the yy-axis. A circle of radius r>sr>s is tangent to both axes and to the second and third circles. What is r/sr/s? [asy] draw((0,25)--(0,0)--(25,0),linewidth(0.7)); draw(Circle((1,1),1),linewidth(0.7)); draw(Circle((3,1),1),linewidth(0.7)); draw(Circle((1,3),1),linewidth(0.7)); draw(Circle((9,9),9),linewidth(0.7)); draw((1,3)--(1,4),dashed); draw((9,9)--(9,0),dashed); draw((-1,3.5)--(1,3.5),dashed); label("ss",(-1,3.5),W); label("rr",(9,4.5),E); [/asy]
Plain-text mathematical notation (without MathML)
Three circles of radius s are drawn in the first quadrant of the xy-plane. The first circle is tangent to both axes, the second is tangent to the first circle and the x-axis, and the third is tangent to the first circle and the y-axis. A circle of radius r>s is tangent to both axes and to the second and third circles. What is r/s?

[asy]
draw((0,25)--(0,0)--(25,0),linewidth(0.7));
draw(Circle((1,1),1),linewidth(0.7));
draw(Circle((3,1),1),linewidth(0.7));
draw(Circle((1,3),1),linewidth(0.7));
draw(Circle((9,9),9),linewidth(0.7));
draw((1,3)--(1,4),dashed);
draw((9,9)--(9,0),dashed);
draw((-1,3.5)--(1,3.5),dashed);
label("s",(-1,3.5),W);
label("r",(9,4.5),E);
[/asy]
Original LaTeX notation
Three circles of radius $s$ are drawn in the first quadrant of the $xy$-plane. The first circle is tangent to both axes, the second is tangent to the first circle and the $x$-axis, and the third is tangent to the first circle and the $y$-axis. A circle of radius $r>s$ is tangent to both axes and to the second and third circles. What is $r/s$?

[asy]
draw((0,25)--(0,0)--(25,0),linewidth(0.7));
draw(Circle((1,1),1),linewidth(0.7));
draw(Circle((3,1),1),linewidth(0.7));
draw(Circle((1,3),1),linewidth(0.7));
draw(Circle((9,9),9),linewidth(0.7));
draw((1,3)--(1,4),dashed);
draw((9,9)--(9,0),dashed);
draw((-1,3.5)--(1,3.5),dashed);
label("$s$",(-1,3.5),W);
label("$r$",(9,4.5),E);
[/asy]

level

Level 5

type

Geometry

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Source and history

task_id
161e0c28-f0c2-528b-ab39-a5fecdd34b0d
task_key
geometry--test--161e0c28-f0c2-528b-ab39-a5fecdd34b0d
task_revision_id
1
config / split
geometry / test

Official source

initial import