Difference between revisions of "2000 AIME II Problems/Problem 12"
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== Problem == | == Problem == | ||
| − | + | The points <math>A</math>, <math>B</math> and <math>C</math> lie on the surface of a sphere with center <math>O</math> and radius <math>20</math>. It is given that <math>AB=13</math>, <math>BC=14</math>, <math>CA=15</math>, and that the distance from <math>O</math> to triangle <math>ABC</math> is <math>\frac{m\sqrt{n}}k</math>, where <math>m</math>, <math>n</math>, and <math>k</math> are positive integers, <math>m</math> and <math>k</math> are relatively prime, and <math>n</math> is not divisible by the square of any prime. Find <math>m+n+k</math>. | |
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== Solution == | == Solution == | ||
Revision as of 19:40, 11 November 2007
Problem
The points 
, 
and 
lie on the surface of a sphere with center 
and radius 
. It is given that 
, 
, 
, and that the distance from to triangle 
is 
, where 
, 
, and 
are positive integers, and are relatively prime, and is not divisible by the square of any prime. Find 
.
Solution
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See also
| 2000 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 11 |
Followed by Problem 13 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
