2022 AIME I Problems/Problem 10
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
.
solution 1
Let the distance between the center of the sphere to the center of those circular intersections as separately.
. According to the problem, we have
. After solving we have
, plug this back to
The desired value is
~bluesoul
See Also
2022 AIME I (Problems • Answer Key • Resources) | ||
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Followed by Problem 11 | |
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