Difference between revisions of "2020 AIME I Problems"
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==Problem 1== | ==Problem 1== | ||
In <math>\triangle{ABC}</math> with <math>AB = AC</math>, point <math>D</math> lies strictly between <math>A</math> and <math>C</math> on side <math>\overline{AC}</math>, and point <math>E</math> lies strictly between <math>A</math> and <math>B</math> on side <math>\overline{AB}</math> such that <math>AE=ED=DB=BC</math>. The degree measure of <math>\angle{ABC}</math> is <math>\frac{m}{n}</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m</math> + <math>n</math>. | In <math>\triangle{ABC}</math> with <math>AB = AC</math>, point <math>D</math> lies strictly between <math>A</math> and <math>C</math> on side <math>\overline{AC}</math>, and point <math>E</math> lies strictly between <math>A</math> and <math>B</math> on side <math>\overline{AB}</math> such that <math>AE=ED=DB=BC</math>. The degree measure of <math>\angle{ABC}</math> is <math>\frac{m}{n}</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m</math> + <math>n</math>. | ||
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[[2020 AIME I Problems/Problem 1 | Solution]] | [[2020 AIME I Problems/Problem 1 | Solution]] | ||
Revision as of 14:45, 12 March 2020
| 2020 AIME I (Answer Key) | AoPS Contest Collections • PDF | ||
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Instructions
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| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
to 
, inclusive. Your score will be the number of correct answers; i.e., there is neither partial credit nor a penalty for wrong answers.Contents
Problem 1
In 
with 
, point 
lies strictly between 
and 
on side 
, and point 
lies strictly between and 
on side 
such that 
. The degree measure of 
is 
, where 
and 
are relatively prime positive integers. Find + .
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
| 2020 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by 2019 AIME II |
Followed by 2020 AIME II | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
