2024 USAMO Problems/Problem 5
- The following problem is from both the 2024 USAMO/5 and 2024 USAJMO/6, so both problems redirect to this page.
Contents
[hide]Problem
Point is selected inside acute triangle so that and . Point is chosen on ray so that . Let be the midpoint of . Show that line is tangent to the circumcircle of triangle .
Solution 1
Let and . Extend AD intersects BC at point T, then TC = TA, TE is perpendicular to AC
Thus, AB is the tangent of the circle BEM
Then the question is equivalent as the is the auxillary angle of .
continue
See Also
2024 USAMO (Problems • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
1 • 2 • 3 • 4 • 5 • 6 | ||
All USAMO Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.