Distance to a Circle

Geometry Level 3

Given circle \(\Gamma\) and a point \(P\) outside of \(\Gamma\), 2 lines \(l_1\) and \(l_2\) are drawn such that both pass through \(P\). \(l_1\) intersects \(\Gamma\) at \(A\) and \(B\), and \(l_2\) intersects \(\Gamma\) at \( C\) and \(D\), with \(C\) between \(D\) and \(P\). If \( PA = 44, PB = 294\) and \(PC = 56 \), what is \( PD\)?

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