Tricky Triangle Problem

Geometry Level 3

In the diagram with coordinates as shown, \(AC = 51\) and \(BC= 55\). The ratio of the area of \(\triangle PAB\) to the area of \(\triangle PAC\) to the area of \(\triangle PBC \) is \(1:2:3\). Determine the ordered pair that represents point \(P \). Express your answer as an ordered pair \((k,w)\) with each member of the ordered pair expressed as a common or improper fraction reduced to the lowest terms.

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