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Difference between revisions of "2024 USAJMO Problems/Problem 6"
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==See Also==
 
==See Also==
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{{USAJMO newbox|year=2024|num-b=5|num-a=Last Question}}
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{{MAA Notice}} of triangle <math>BEM</math>.
 
{{MAA Notice}} of triangle <math>BEM</math>.

Revision as of 12:41, 23 March 2024

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.

Solution 1

See Also

2024 USAJMO (Problems • Resources)
Preceded by
Problem 5 		Followed by
Last Question
1 • 2 • 3 • 4 • 5 • 6
All USAJMO Problems and Solutions

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of triangle $BEM$.

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