# 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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