Difference between revisions of "2024 USAJMO Problems/Problem 6"

Latest revision as of 11:20, 24 March 2024

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-__TOC__
+#REDIRECT [[2024 USAMO Problems/Problem 5]]
-== Problem ==
-Point <math>D</math> is selected inside acute triangle <math>ABC</math> so that <math>\angle DAC=\angle ACB</math> and <math>\angle BDC=90^\circ+\angle BAC</math>. Point <math>E</math> is chosen on ray <math>BD</math> so that <math>AE=EC</math>. Let <math>M</math> be the midpoint of <math>BC</math>. Show that line <math>AB</math> is tangent to the circumcircle.
-== Solution 1 ==
-==See Also==
-{{USAJMO newbox|year=2024|num-b=5|after=Last Question}}
-{{MAA Notice}} of triangle <math>BEM</math>.