Difference between revisions of "2024 AMC 12A Problems/Problem 19"
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==Solution 2 (Law of Cosines + Law of Sines)== | ==Solution 2 (Law of Cosines + Law of Sines)== |
Latest revision as of 17:31, 17 November 2024
Contents
[hide]Problem
Cyclic quadrilateral has lengths and with . What is the length of the shorter diagonal of ?
Solution 1
~diagram by erics118
First, by properties of cyclic quadrilaterals.
Let . Apply the Law of Cosines on :
Let . Apply the Law of Cosines on :
By Ptolemy’s Theorem, Since , The answer is .
~lptoggled, formatting by eevee9406, typo fixed by meh494
Solution 2 (Law of Cosines + Law of Sines)
Draw diagonals and . By Law of Cosines,
~evanhliu2009
Video Solution by SpreadTheMathLove
https://www.youtube.com/watch?v=f32mBtYTZp8
See also
2024 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 18 |
Followed by Problem 20 |
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.