Difference between revisions of "2024 USAJMO Problems/Problem 6"
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| − | + | __TOC__ | |
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| + | == 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. | ||
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| + | == Solution 1 == | ||
| + | |||
| + | |||
| + | ==See Also== | ||
| + | {{USAJMO newbox|year=2024|num-b=5|num-a=Last Question}} | ||
| + | {{MAA Notice}} of triangle <math>BEM</math>. | ||
Revision as of 12:41, 23 March 2024
Contents
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.
Solution 1
See Also
| 2024 USAJMO (Problems • Resources) | ||
| Preceded by Problem 5 |
Followed by Problem Last Question | |
| 1 • 2 • 3 • 4 • 5 • 6 | ||
| All USAJMO Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
of triangle 
.
