1955 AMC 12 Question 44 - thichhoctoan.com

Question 44

In circle $O$ chord $\overline{AB}$ is produced so that $\overline{BC}$ equals a radius of the circle. $\overline{CO}$ is drawn and extended to $D.$ $\overline{AO}$ is drawn. Which of the following expresses the relationship between angles $x$ and $y?$

Question illustration

$x=3y$
$x=2y$
$x=60^\circ$
there is no special relationship between $x$ and $y$
$x=2y$ or $x=3y,$ depending upon the length of
$\overline{AB}$