Difference between revisions of "2017 USAJMO Problems/Problem 5"

(Created page with "==Problem== Let <math>O</math> and <math>H</math> be the circumcenter and the orthocenter of an acute triangle <math>ABC</math>. Points <math>M</math> and <math>D</math> lie...")
 
Line 4: Line 4:
  
 
==Solution==
 
==Solution==
 +
 +
{{MAA Notice}}
 +
 +
==See also==
 +
{{USAJMO newbox|year=2017|num-b=1|num-a=3}}

Revision as of 19:35, 20 April 2017

Problem

Let $O$ and $H$ be the circumcenter and the orthocenter of an acute triangle $ABC$. Points $M$ and $D$ lie on side $BC$ such that $BM = CM$ and $\angle BAD = \angle CAD$. Ray $MO$ intersects the circumcircle of triangle $BHC$ in point $N$. Prove that $\angle ADO = \angle HAN$.

Solution

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

See also

2017 USAJMO (ProblemsResources)
Preceded by
Problem 1
Followed by
Problem 3
1 2 3 4 5 6
All USAJMO Problems and Solutions