Difference between revisions of "2021 AIME II Problems/Problem 10"
Etmetalakret (talk | contribs) (Created page with "==Problem== These problems will not be posted until the 2021 AIME II is released on Thursday, March 25, 2021. ==Solution== We can't have a solution without a problem. ==See a...") |
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==Problem== | ==Problem== | ||
| − | + | Two spheres with radii <math>36</math> and one sphere with radius <math>13</math> are each externally tangent to the other two spheres and to two different planes <math>\mathcal{P}</math> and <math>\mathcal{Q}</math>. The intersection of planes <math>\mathcal{P}</math> and <math>\mathcal{Q}</math> is the line <math>\ell</math>. The distance from line <math>\ell</math> to the point where the sphere with radius <math>13</math> is tangent to plane <math>\mathcal{P}</math> is <math>\tfrac{m}{n}</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m + n</math>. | |
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==Solution== | ==Solution== | ||
We can't have a solution without a problem. | We can't have a solution without a problem. | ||
Revision as of 14:57, 22 March 2021
Problem
Two spheres with radii 
and one sphere with radius 
are each externally tangent to the other two spheres and to two different planes 
and 
. The intersection of planes and is the line 
. The distance from line to the point where the sphere with radius is tangent to plane is 
, where 
and 
are relatively prime positive integers. Find 
.
Solution
We can't have a solution without a problem.
See also
| 2021 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 9 |
Followed by Problem 11 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
