Difference between revisions of "2001 IMO Problems/Problem 5"
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Latest revision as of 14:01, 15 May 2024
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[hide]Problem
is a triangle. lies on and bisects angle . lies on and bisects angle . Angle is . . Find all possible values for angle .
Solution1
Let be on extension of and . Let be on and , then Since , is equilateral. Let , then, We claim that must be on , i.e., . If is not on , then , which leads to , and is equilateral, which is not possible. With that, we have, in , , , and .
Solution by .
Solution 2
Refer to the image in Solution 1 without any construction
~Lakshya Pamecha
Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.
See also
2001 IMO (Problems) • Resources | ||
Preceded by Problem 4 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 6 |
All IMO Problems and Solutions |