CAPS 2009 Problem 3

Let $\omega$ denote the excircle tangent to side $BC$ of triangle $ABC$ . A line $\ell$ parallel to $BC$ meets sides $AB$ and $AC$ at points $D$ and $E$ , respectively. Let $\omega'$ denote the incircle of triangle $ADE$ . The tangent from $D$ to $\omega$ (different from line $AB$ ) and the tangent from $E$ to $\omega$ (different from line $AC$ ) meet at point $P$ . The tangent from $B$ to $\omega'$ (different from line $AB$ ) and the tangent from $C$ to $\omega'$ (different from line $AC$ ) meet at point $Q$ . Prove that, independent of the choice of $\ell$ , there is a fixed point that line $PQ$ always passes through.