2012 China TST Quiz1-Da2-p4
Posted: Fri Mar 23, 2012 10:58 am
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.