Difference between revisions of "2023 AMC 10B Problems"
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==Problem 3== | ==Problem 3== | ||
A <math>3-4-5</math> right triangle is inscribed in circle <math>A</math>, and a <math>5-12-13</math> right triangle is inscribed in circle <math>B</math>. What is the ratio of the area of circle <math>A</math> to the area of circle <math>B</math>? | A <math>3-4-5</math> right triangle is inscribed in circle <math>A</math>, and a <math>5-12-13</math> right triangle is inscribed in circle <math>B</math>. What is the ratio of the area of circle <math>A</math> to the area of circle <math>B</math>? | ||
| + | <math>\textbf{(A) }\frac{1}{9}\qquad\textbf{(B) }\frac{25}{169}\qquad\textbf{(C) }\frac{4}{25}\qquad\textbf{(D) }\frac{1}{5}\qquad\textbf{(E) }\frac{9}{25}</math> | ||
[[2023 AMC 10B Problems/Problem 3|Solution]] | [[2023 AMC 10B Problems/Problem 3|Solution]] | ||
Revision as of 14:57, 15 November 2023
| 2023 AMC 10B (Answer Key) Printable versions: • AoPS Resources • 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 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
Contents
- 1 Problem 1
- 2 Problem 2
- 3 Problem 3
- 4 Problem 4
- 5 Problem 5
- 6 Problem 6
- 7 Problem 7
- 8 Problem 8
- 9 Problem 9
- 10 Problem 10
- 11 Problem 11
- 12 Problem 12
- 13 Problem 13
- 14 Problem 14
- 15 Problem 15
- 16 Problem 16
- 17 Problem 17
- 18 Problem 18
- 19 Problem 19
- 20 Problem 20
- 21 Problem 21
- 22 Problem 22
- 23 Problem 23
- 24 Problem 24
- 25 Problem 25
- 26 See also
Problem 1
Mrs. Jones is pouring orange juice into four identical glasses for her four sons. She fills the first three glasses completely but runs out of juice when the fourth glass is only 
full. What fraction of a glass must Mrs. Jones pour from each of the first three glasses into the fourth glass so that all four glasses will have the same amount of juice?
Problem 2
Problem 3
A 
right triangle is inscribed in circle 
, and a 
right triangle is inscribed in circle 
. What is the ratio of the area of circle to the area of circle ?
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
What is the perimeter of the boundary of the region consisting of all points which can be expressed as 
with 
, 
and 
?
Problem 25
A regular pentagon with area 
is printed on paper and cut out. All five vertices are folded to the center of the pentagon, creating a smaller pentagon. What is the area of the new pentagon?
See also
| 2023 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by 2022 AMC 10A Problems |
Followed by 2024 AMC 10A Problems | |
| 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 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
