Points of tangency and concyclic

01092011, 07:50 PM
Post: #1




Points of tangency and concyclic
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[/float]See the picture，given $\triangle ABC$ and its excircle $\odot I_a$，let $\ell_1$、$\ell_2$ the common tangents of $\odot O(ABC)$ and $\odot I_a$ that cut $BC$ at $D$、$E$; let $P$、$Q$ on $\odot O$ be the tangent poins，and $I_b$、$I_c$ be the other escenters of $\triangle ABC$ .
Prove that： (1): $P$、$Q$、$I_b$、$I_c$ are on a circle. (2): $\angle BAD=\angle CAE$ . 

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