2012 China TST Quiz1-Da2-p4

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Tahmid Hasan
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2012 China TST Quiz1-Da2-p4

Unread post by Tahmid Hasan » 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.
বড় ভালবাসি তোমায়,মা

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