2024 USAJMO Problems/Problem 6

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 $BEM$ .

2024 USAJMO (Problems • Resources)
Preceded by Problem 5	Followed by Last Question
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2024 USAJMO Problems/Problem 6

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Problem

Solution 1

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