A little point

Geometry Level 4

In \(\triangle ABC\) let \(AB=BC=L\) and \(\angle ABC = 90°\). There is a point \(Q\) inside \(\triangle ABC\) such that \(QA=k\), \(QB=2k\) and \(QC=3k\). If \(\left(\dfrac{L}{k}\right)^2=a+b\sqrt{c}\), where \(a\), \(b\) and \(c\) are natural numbers and \(c\) is prime, find \(a+b+c\).

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