Difference between revisions of "2005 AMC 12A Problems/Problem 16"
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== Problem == | == Problem == | ||
− | Three [[circle]]s of [[radius]] <math> | + | Three [[circle]]s of [[radius]] <math>s</math> are drawn in the first [[quadrant]] of the <math>xy</math>-[[plane]]. The first circle is tangent to both axes, the second is [[tangent (geometry)|tangent]] to the first circle and the <math>x</math>-axis, and the third is tangent to the first circle and the <math>y</math>-axis. A circle of radius <math>r > s</math> is tangent to both axes and to the second and third circles. What is <math>r/s</math>? |
<asy> | <asy> | ||
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<math> (\mathrm {A}) \ 5 \qquad (\mathrm {B}) \ 6 \qquad (\mathrm {C})\ 8 \qquad (\mathrm {D}) \ 9 \qquad (\mathrm {E})\ 10 </math> | <math> (\mathrm {A}) \ 5 \qquad (\mathrm {B}) \ 6 \qquad (\mathrm {C})\ 8 \qquad (\mathrm {D}) \ 9 \qquad (\mathrm {E})\ 10 </math> | ||
− | == | + | == See also == |
+ | {{AMC12 box|year=2005|num-b=15|num-a=17|ab=A}} | ||
− | + | [[Category:Introductory Geometry Problems]] | |
− | [[ | + | {{MAA Notice}} |
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Latest revision as of 16:22, 19 August 2024
Problem
Three circles of radius are drawn in the first quadrant of the
-plane. The first circle is tangent to both axes, the second is tangent to the first circle and the
-axis, and the third is tangent to the first circle and the
-axis. A circle of radius
is tangent to both axes and to the second and third circles. What is
?
See also
2005 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 15 |
Followed by Problem 17 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.