ITOT 43 Autumn 2021 - THPT A - additive practice Question 5

Point $P$ lies inside parallelogram $ABCD$ and satisfies $\angle PDA=\angle PBA$. Let $\omega_1$ be the excircle opposite $A$ of triangle $PAB$, and $\omega_2$ the incircle of triangle $PCD$. Prove that these circles have a common tangent parallel to $AD$. (9 points)



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