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 Orthocenter property
Сообщение15.10.2012, 02:55 
Аватара пользователя
Let aqute-angled triangle $ABC$ with orhtocenter $H$ is inscribed in circle $k$. Through $H$ is drawn line $l$. $M$ and $N$ are the intersection points of $l$ with the sides $AC$ and $BC$. $k'$ is a circle through $M$, $N$ and $C$. $P$ is the second intersection point of $k$ and $k'$. Through $P$ and $H$ is drawn line intersecting $k'$ at the point $Q$. Prove that $MN \perp CQ$.

 
 
 
 Re: Orthocenter property
Сообщение19.10.2012, 00:45 
Аватара пользователя
http://www.artofproblemsolving.com/Foru ... 8&t=502451
you can see two solutions of the problem.

 
 
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