Difference between revisions of "1993 AHSME Problems/Problem 8"
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== Solution == | == Solution == | ||
+ | There are two radius 3 circles to which <math>C_1</math> and <math>C_2</math> are both externally tangent. One touches the tops of <math>C_1</math> and <math>C_2</math> and extends upward, and the other the other touches the bottoms and extends downward. There are also two radius 3 circles to which <math>C_1</math> and <math>C_2</math> are both internally tangent, one touching the tops and encircling downward, and the other touching the bottoms and encircling upward. There are two radius 3 circles passing through the point where <math>C_1</math> and <math>C_2</math> are tangent. For one <math>C_1</math> is internally tangent and <math>C_2</math> is externally tangent, and for the other <math>C_2</math> is externally tangent and <math>C_1</math> is internally tangent. | ||
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<math>\fbox{D}</math> | <math>\fbox{D}</math> | ||
Revision as of 20:58, 27 May 2021
Problem
Let and be circles of radius 1 that are in the same plane and tangent to each other. How many circles of radius 3 are in this plane and tangent to both and ?
Solution
There are two radius 3 circles to which and are both externally tangent. One touches the tops of and and extends upward, and the other the other touches the bottoms and extends downward. There are also two radius 3 circles to which and are both internally tangent, one touching the tops and encircling downward, and the other touching the bottoms and encircling upward. There are two radius 3 circles passing through the point where and are tangent. For one is internally tangent and is externally tangent, and for the other is externally tangent and is internally tangent.
See also
1993 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
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 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
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