Trisected triangle

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 $a+b$ .