NMQ's Mathematical Memoir

(Lướt xuống sẽ thấy phần tiếng Việt, hình được đính kèm ở cuối blog) -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --  -- -- -- -- -- -- -- -- --  A property of the Euler-Poncelet Point An apprentice of mine (Dương Phú Tài) sent me this corollary from a problem composed by Lê Trung Hiếu: Given a complete quadrilateral $ABCD.EF$ with $ABCD$ being concyclic, define $P$ as the Euler-Poncelet point. $O$, $H$ respectively are the circumcenter and orthocenter of $\Delta AEC$. $O'$, $H'$ are defined similarly for $\Delta AFC$.  a) Prove that the midpoint of segment $AC$ lies on the Gauss-Newton line, defined as line $\omega$ of quadrilateral $HOH'O'$ b) Prove that $P$ lies on $\omega$ - Euler-Poncelet Point: The intersection of the Euler Circles of $\Delta ABC, ABD, ACD, BCD$ Although this problem could be stated more clearly, it is nonetheless an interesting issue. The Euler-Poncelet point is not a very explored problem in synthetic geometry, so I hope this prop...

Hello everyone, welcome to my Mathematics blog, where all sorts of mathematically-induced highs get manifested into a form of yapping. I'm not going to say as much as my English blog, due to the nature of the blog and the fact that I have to translate this into Vietnamese, which I loathe. However, there are a few key rules of procedure, as well as how this blog will function, that I would like to take into account. 1. Don’t shame, bully, or act in bad faith regarding the blog or me as a result of this blog. I am here to share my thoughts, not to wage conflict.  2. Do discuss the subject in the reply section or inbox me (highly recommend replying) if you have any points of information available to raise, or to discuss literally anything slightly relevant.  3. Do civilly raise complaints and/or feedback.  4. Don’t uncivilly raise complaints and/or feedback.  5. Do have fun, and if you are compelled to, like, reply and maybe, just maybe share? There is no set them...