Difference between revisions of "2022 AIME I Problems/Problem 10"
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| − | . | + | == Problem == |
| + | Three spheres with radii <math>11</math>, <math>13</math>, and <math>19</math> are mutually externally tangent. A plane intersects the spheres in three congruent circles centered at <math>A</math>, <math>B</math>, and <math>C</math>, respectively, and the centers of the spheres all lie on the same side of this plane. Suppose that <math>AB^2 = 560</math>. Find <math>AC^2</math>. | ||
| + | |||
| + | ==See Also== | ||
| + | {{AIME box|year=2022|n=I|num-b=9|num-a=11}} | ||
| + | {{MAA Notice}} | ||
Revision as of 20:22, 17 February 2022
Problem
Three spheres with radii 
, 
, and 
are mutually externally tangent. A plane intersects the spheres in three congruent circles centered at 
, 
, and 
, respectively, and the centers of the spheres all lie on the same side of this plane. Suppose that 
. Find 
.
See Also
| 2022 AIME I (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. 
