1954 AMC 12 Question 47 - thichhoctoan.com

Question 47

At the midpoint of line segment $\overline{AB}$ which is $p$ units long, a perpendicular $\overline{MR}$ is erected with length $q$ units. An arc is described from $R$ with a radius equal to $\dfrac12\overline{AB},$ meeting $\overline{AB}$ at $T.$ Then $\overline{AT}$ and $\overline{TB}$ are the roots of:

$x^2+px+q^2=0$
$x^2-px+q^2=0$
$x^2+px-q^2=0$
$x^2-px-q^2=0$
$x^2-px+q=0$