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2024 USAMO Problems/Problem 5

Revision as of 21:30, 20 March 2024 by Anyu-tsuruko (talk | contribs) (Created page with "Point <math>D</math> is selected inside acute triangle <math>A B C</math> so that <math>\angle D A C=</math> <math>\angle A C B</math> and <math>\angle B D C=90^{\circ}+\angle...")
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Point $D$ is selected inside acute triangle $A B C$ so that $\angle D A C=$ $\angle A C B$ and $\angle B D C=90^{\circ}+\angle B A C$. Point $E$ is chosen on ray $B D$ so that $A E=E C$. Let $M$ be the midpoint of $B C$. Show that line $A B$ is tangent to the circumcircle of triangle $B E M$.

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