Difference between revisions of "2021 AMC 12A Problems/Problem 24"
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<math>\textbf{(A) } 110\qquad\textbf{(B) } 114\qquad\textbf{(C) } 118\qquad\textbf{(D) } 122\qquad\textbf{(E) } 126\qquad</math> | <math>\textbf{(A) } 110\qquad\textbf{(B) } 114\qquad\textbf{(C) } 118\qquad\textbf{(D) } 122\qquad\textbf{(E) } 126\qquad</math> | ||
| + | |||
| + | ==Diagram== | ||
| + | [[File:2021 AMC 12A Problem 24.png|center]] | ||
| + | ~MRENTHUSIASM (by Geometry Expressions) | ||
==Video Solution by Punxsutawney Phil== | ==Video Solution by Punxsutawney Phil== | ||
Revision as of 01:52, 14 February 2021
Contents
Problem
Semicircle 
has diameter 
of length 
. Circle 
lies tangent to at a point 
and intersects at points 
and 
. If 
and 
, then the area of 
equals 
, where 
and 
are relatively prime positive integers, and 
is a positive integer not divisible by the square of any prime. What is 
?
Diagram
~MRENTHUSIASM (by Geometry Expressions)
Video Solution by Punxsutawney Phil
https://youtube.com/watch?v=cEHF5iWMe9c
Video Solution by OmegaLearn (Similar Triangles, Law of Sines, Law of Cosines )
See also
| 2021 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 23 |
Followed by Problem 25 |
| 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. 
