2024 USAMO Problems/Problem 5: Difference between revisions
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Point <math>D</math> is selected inside acute triangle <math> | __TOC__ | ||
Show that line <math> | |||
== 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 of triangle <math>BEM</math>. | |||
== Solution 1 == | |||
==See Also== | |||
{{USAMO newbox|year=2024|num-b=4|num-a=6}} | |||
{{MAA Notice}} | |||
Revision as of 10:21, 24 March 2024
Problem
Point 
is selected inside acute triangle 
so that 
and 
. Point 
is chosen on ray 
so that 
. Let 
be the midpoint of 
. Show that line 
is tangent to the circumcircle of triangle 
.
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 | ||
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