Proposed by \(Marek\) \(Pechal.\)

Geometry Level 5

In \(\triangle ABC\) the bisector of \(\angle BCA\) intersects the \(\odot ABC\) again at \(R\), the perpendicular bisector of \(BC\) at \(P\), and the perpendicular bisector of \(AC\) at \(Q\). The midpoint of \(BC\) is \(K\) and the midpoint of \(AC\) is \(L\). Given that \(Ar.\Delta RPK\) is \(16.4\) sq. units. Find the value of \(Ar.\Delta RPK\times Ar.\Delta RQL\), rounded to the nearest integer.

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