Difference between revisions of "2021 AIME II Problems/Problem 10"
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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 15:57, 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.