Trisected triangle

Geometry Level 3

A right triangle \(PQR\), has its hypotenuse, \(PR\), trisected at points \(A\) and \(B\). Two lines, (QA) and \(QB\) are then drawn and \(k\) is such that \(QA^2 + QB^2 = (PR^2) * k\). If \(k\) can be expressed as \(\dfrac{a}{b}\) where HCF(\(a,b\))=\(1\)Find the value of \(a+b\).

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