2022 AMC 12B Problems/Problem 19
Problem
In medians
and
intersect at
and
is equilateral. Then
can be written as
, where
and
are relatively prime positive integers and
is a positive integer not divisible by the square of any prime. What is
?
Solution 1: Law of Cosines
Note: can someone add the diagram here please, I don't know how to do that
Let . Since
is the midpoint of
,
must also be
.
Since the centroid splits the median in a ratio,
must be equal to
and
must be equal to
.
Applying Law of Cosines on and
yields
and
. Finally, applying Law of Cosines on
yields
. The requested sum is
.
See Also
2022 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 18 |
Followed by Problem 20 |
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