Difference between revisions of "2022 AIME II Problems/Problem 7"
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A circle with radius <math>6</math> is externally tangent to a circle with radius <math>24</math>. Find the area of the triangular region bounded by the three common tangent lines of these two circles. | A circle with radius <math>6</math> is externally tangent to a circle with radius <math>24</math>. Find the area of the triangular region bounded by the three common tangent lines of these two circles. | ||
| + | |||
| + | ==Solution 1== | ||
| + | |||
| + | <asy> | ||
| + | import graph; | ||
| + | |||
| + | path t1, t2, t3; | ||
| + | draw(circle((0,0),24)); | ||
| + | draw(circle((30,0),6)); | ||
| + | draw((72/5, 96/5) -- (40,0)); | ||
| + | draw((72/5, -96/5) -- (40,0)); | ||
| + | |||
| + | </asy> | ||
| + | |||
| + | To be continued...... | ||
| + | |||
| + | ~[https://artofproblemsolving.com/wiki/index.php/User:Isabelchen isabelchen] | ||
==Video Solution (Mathematical Dexterity)== | ==Video Solution (Mathematical Dexterity)== | ||
Revision as of 05:44, 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] import graph; path t1, t2, t3; draw(circle((0,0),24)); draw(circle((30,0),6)); draw((72/5, 96/5) -- (40,0)); draw((72/5, -96/5) -- (40,0)); [/asy]](http://latex.artofproblemsolving.com/7/8/3/78318970b5d411ca801909735c20415127cbf572.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. 
