## 2012 China TST Quiz1-Da2-p4

For students of class 11-12 (age 16+)
Tahmid Hasan
Posts: 665
Joined: Thu Dec 09, 2010 5:34 pm
Given two circles $\omega _1,\omega_2$.$S$ denotes all $\triangle ABC$ satisfies that $\omega _1$ is the circumcircle and $\omega _2$ is the $A$-excircle of $\triangle ABC$.$\omega _2$ touches $BC,CA,AB$ at $D,E,F$ respectively.Prove that the centroid of $\triangle DEF$ is a fixed point.