# 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 $$a+b$$.

×