Difference between revisions of "2008 USAMO Problems/Problem 2"
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[[Category:Olympiad Geometry Problems]] | [[Category:Olympiad Geometry Problems]] | ||
Revision as of 18:57, 1 May 2008
Problem
(Zuming Feng) Let 
be an acute, scalene triangle, and let 
, 
, and 
be the midpoints of 
, 
, and 
, respectively. Let the perpendicular bisectors of and 
intersect ray 
in points 
and 
respectively, and let lines 
and 
intersect in point 
, inside of triangle . Prove that points 
, , , and all lie on one circle.
Solution
Solution 1
Solution 2
Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.
Resources
| 2008 USAMO (Problems • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 1 • 2 • 3 • 4 • 5 • 6 | ||
| All USAMO Problems and Solutions | ||
- <url>viewtopic.php?t=202907 Discussion on AoPS/MathLinks</url>
