Difference between revisions of "2022 AIME II Problems/Problem 7"
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<asy> | <asy> | ||
//Created by isabelchen | //Created by isabelchen | ||
| + | |||
| + | size(12cm, 12cm); | ||
draw(circle((0,0),24)); | draw(circle((0,0),24)); | ||
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label("$O_1$",(0, 0),S); | label("$O_1$",(0, 0),S); | ||
dot((30, 0)); | dot((30, 0)); | ||
| − | label("$O_2$",(30, | + | label("$O_2$",(30, 0),S); |
</asy> | </asy> | ||
Revision as of 07:59, 19 February 2022
Problem
A circle with radius 
is externally tangent to a circle with radius 
. Find the area of the triangular region bounded by the three common tangent lines of these two circles.
Solution 1
![[asy] //Created by isabelchen size(12cm, 12cm); draw(circle((0,0),24)); draw(circle((30,0),6)); draw((72/5, 96/5) -- (40,0)); draw((72/5, -96/5) -- (40,0)); draw((24, 12) -- (24, -12)); draw((0, 0) -- (40, 0)); draw((72/5, 96/5) -- (0,0)); draw((168/5, 24/5) -- (30,0)); draw((54/5, 72/5) -- (30,0)); dot((72/5, 96/5)); label("$A$",(72/5, 96/5),NE); dot((168/5, 24/5)); label("$B$",(168/5, 24/5),NE); dot((24,0)); label("$C$",(24,0),NW); dot((40, 0)); label("$D$",(40, 0),NE); dot((24, 12)); label("$E$",(24, 12),NE); dot((0, 0)); label("$O_1$",(0, 0),S); dot((30, 0)); label("$O_2$",(30, 0),S); [/asy]](http://latex.artofproblemsolving.com/e/e/5/ee5e15700217d43902faf846f8f4616ac0b54080.png)
To be continued......
Video Solution (Mathematical Dexterity)
https://www.youtube.com/watch?v=7NGkVu0kE08
See Also
| 2022 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 6 |
Followed by Problem 8 | |
| 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. 
