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2024 USAMO Problems/Problem 5: Difference between revisions

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{{duplicate|[[2024 USAMO Problems/Problem 5|2024 USAMO/5]] and [[2024 USAJMO Problems/Problem 6|2024 USAJMO/6]]}}
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Revision as of 10:23, 24 March 2024

The following problem is from both the 2024 USAMO/5 and 2024 USAJMO/6, so both problems redirect to this page.

Problem

Point $D$ is selected inside acute triangle $ABC$ so that $\angle DAC=\angle ACB$ and $\angle BDC=90^\circ+\angle BAC$. Point $E$ is chosen on ray $BD$ so that $AE=EC$. Let $M$ be the midpoint of $BC$. Show that line $AB$ is tangent to the circumcircle of triangle $BEM$.

Solution 1

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

These problems are copyrighted © by the Mathematical Association of America.

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