1969 AMC 12 Question 15 - thichhoctoan.com

Question 15

In a circle with center at $O$ and radius $r,$ chord $AB$ is drawn with length equal to $r$ units. From $O$ a perpendicular to $AB$ meets $AB$ at $M.$ From $M$ a perpendicular to $OA$ meets $OA$ at $D.$ In terms of $r,$ the area of triangle $MDA,$ in appropriate square units, is:

$\dfrac{3r^2}{16}$
$\dfrac{\pi r^2}{16}$
$\dfrac{\pi r^2\sqrt2}{8}$
$\dfrac{r^2\sqrt3}{32}$
$\dfrac{r^2\sqrt6}{48}$