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Geometry Difficulty 8.0 Shortlist Prove it Hungary

Two circles are given in the plane, $\Omega$ and inside it $\omega$ . The center of $\omega$ is $I$ . $P$ is a point moving on $\Omega$ . The second intersection of the tangents from $P$ to $\omega$ and circle $\Omega$ are $Q$ and $R$ . The second intersection of circle $IQR$ and lines $PI$ , $PQ$ and $PR$ are $J$ , $S$ and $T$ , respectively. The reflection of point $J$ across line $ST$ is $K$ .

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