IRAN 1995
Posted: 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 $\Delta ABC$.