Trisection of an angle

Instructions:
Move [b]Point B[/b] to change angle [img]data:image/png;base64,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[/img]. To find the trisection of the new [img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAC8AAAAOCAYAAAC/10U/AAAB6ElEQVRIS9WVvyuGURTHP6+RhEyKEIMRk8Gv8hcoxcZgJJTCrlCKYjQwysBiklIMNkZKoQhRGGRR9K17dd7rPu/7PtObZ3zOfc75nO/53vNk+MdPpkjsna7uSYr6+ibrfBr4M2A8SDAJzACPwJYD6QHqgfYI2ALQAlwAT8AYsAPM5WniyMV77blC4TfcR6ORIl/ANLBqYg/AB9Bs3l0BgghzfDp4+70tI8UPgDegJi18LnAlPgZCEQSvabS5YoKuDZrxHJpoeUJMZ3aBKqAVqEwDPwjMGohQeDU2ECSVlbw9bgHfYFfoWdPYHzAXUy4JofgEUFoovIpu5lBEeWSFakDq6akD7oFhQOB6FGsMVctjMR+W6v2AmlgJJ5zkeV24Q6DPQMTuVJLf94235dXrHNP7BvYcpK0hcEFLhFTwGlVHHvAkv8vf3UCJIxH8OZC1KVxMthsBmoJayr0GvJtutMWGgG3/Lqa8xrxoD8UkB2J+91YqM5shvLw+naariSxFVqW3iy2tCU3ZrRbCFwruIe8CRWNKauTLgbrelrHVqRzPkYYEL1F//wkWXglPgcsEpfVaF1GXct5tACnnR1sB3ES8q+/81tLZV6Ah8sOzl/vFLApx6QeojaP36179Qn9SOfopXuhfw/8AnCNxD1DInBsAAAAASUVORK5CYII=[/img], move point C to [b]identify[/b] [b]point D[/b] with the [b]point of intersection[/b] of [math]\begin{matrix}\leftrightarrow\\BC\end{matrix}[/math] and [math]\begin{matrix}\leftrightarrow\\AO\end{matrix}[/math].

Information: Trisection of an angle