Difference between revisions of "2020 AMC 12A Problems/Problem 24"
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giving us that <math>s = \boxed{\textbf{(B) } \sqrt{7}}</math>. ~ciceronii | giving us that <math>s = \boxed{\textbf{(B) } \sqrt{7}}</math>. ~ciceronii | ||
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+ | ==See Also== | ||
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+ | {{AMC12 box|year=2020|ab=A|num-b=8|num-a=10}} | ||
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Revision as of 19:31, 1 February 2020
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 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
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