Difference between revisions of "2022 AIME II Problems/Problem 7"
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draw((72/5, 96/5) -- (40,0)); | draw((72/5, 96/5) -- (40,0)); | ||
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)); | ||
</asy> | </asy> | ||
Revision as of 07:37, 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 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)); [/asy]](http://latex.artofproblemsolving.com/d/a/f/daf36738ebf5927e2a812948548f916cff27d8d0.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 | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
