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Points of tangency and concyclic
01-09-2011, 07:50 PM
Post: #1
Points of tangency and concyclic
[float=right]     [/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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