IRAN 1995

Discussion on Bangladesh National Math Camp
shehab ahmed
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Joined: Tue Mar 20, 2012 12:52 am

IRAN 1995

Unread post by shehab ahmed » Mon May 28, 2012 12:26 am

Let,the in-circle of $\Delta ABC$ touches the sides of the triangle at $D,E,F$. Let $X,Y,Z$ be the midpoints of $DE,EF,FD$.Prove that the line joining the circum-centre of $\Delta XYZ$ and the circum-centre of $\Delta ABC$ goes through the in-centre of $\Delta ABC$.
Last edited by Masum on Tue May 29, 2012 12:38 pm, edited 1 time in total.
Reason: LaTeXed. Also, you should use proper punctuation for your posts.

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FahimFerdous
Posts: 176
Joined: Thu Dec 09, 2010 12:50 am
Location: Mymensingh, Bangladesh

Re: IRAN 1995

Unread post by FahimFerdous » Mon May 28, 2012 8:53 am

It's actually ISL 14 of 1986. A nice one where I used a little inversion and it worked. Remember, inversion keeps the original centre, the inverted centre and the centre of inversion collinear. :-)
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