Let
![A, B](/media/m/a/9/4/a94509f709e0a89fd467927301d3bf18.png)
, and
![C](/media/m/5/a/b/5ab88f3f735b691e133767fe7ea0483c.png)
be three points on the edge of a circular chord such that
![B](/media/m/c/e/e/ceebc05be717fa6aab8e71b02fe3e4e3.png)
is due west of
![C](/media/m/5/a/b/5ab88f3f735b691e133767fe7ea0483c.png)
and
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
is an equilateral triangle whose side is
![86](/media/m/0/2/2/02230df4b38b6a46c02c9c037881e5c9.png)
meters long. A boy swam from
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
directly toward
![B](/media/m/c/e/e/ceebc05be717fa6aab8e71b02fe3e4e3.png)
. After covering a distance of
![x](/media/m/f/1/8/f185adeed9bd346bc960bca0147d7aae.png)
meters, he turned and swam westward, reaching the shore after covering a distance of
![y](/media/m/c/c/0/cc082a07a517ebbe9b72fd580832a939.png)
meters. If
![x](/media/m/f/1/8/f185adeed9bd346bc960bca0147d7aae.png)
and
![y](/media/m/c/c/0/cc082a07a517ebbe9b72fd580832a939.png)
are both positive integers, determine
%V0
Let $A, B$, and $C$ be three points on the edge of a circular chord such that $B$ is due west of $C$ and $ABC$ is an equilateral triangle whose side is $86$ meters long. A boy swam from $A$ directly toward $B$. After covering a distance of $x$ meters, he turned and swam westward, reaching the shore after covering a distance of $y$ meters. If $x$ and $y$ are both positive integers, determine $y.$