2020 AMC 12A Problems/Problem 24
Problem 24
Suppose that is an equilateral triangle of side length
, with the property that there is a unique point
inside the triangle such that
,
, and
. What is
?
Solution
We begin by rotating by
about
, such that in
,
. We see that
is equilateral with side length
, meaning that
. We also see that
is a
right triangle, meaning that
. Thus, by adding the two together, we see that
. We can now use the law of cosines as following:
giving us that . ~ciceronii
See Also
2020 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 8 |
Followed by Problem 10 |
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