IMO Shortlist 1986 problem 3
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Avg: 0,0 Let
, and
be three points on the edge of a circular chord such that
is due west of
and
is an equilateral triangle whose side is
meters long. A boy swam from
directly toward
. After covering a distance of
meters, he turned and swam westward, reaching the shore after covering a distance of
meters. If
and
are both positive integers, determine
![A, B](/media/m/a/9/4/a94509f709e0a89fd467927301d3bf18.png)
![C](/media/m/5/a/b/5ab88f3f735b691e133767fe7ea0483c.png)
![B](/media/m/c/e/e/ceebc05be717fa6aab8e71b02fe3e4e3.png)
![C](/media/m/5/a/b/5ab88f3f735b691e133767fe7ea0483c.png)
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
![86](/media/m/0/2/2/02230df4b38b6a46c02c9c037881e5c9.png)
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
![B](/media/m/c/e/e/ceebc05be717fa6aab8e71b02fe3e4e3.png)
![x](/media/m/f/1/8/f185adeed9bd346bc960bca0147d7aae.png)
![y](/media/m/c/c/0/cc082a07a517ebbe9b72fd580832a939.png)
![x](/media/m/f/1/8/f185adeed9bd346bc960bca0147d7aae.png)
![y](/media/m/c/c/0/cc082a07a517ebbe9b72fd580832a939.png)
![y.](/media/m/9/2/3/923fc0c0f0d7a54598bbd1f90c33b74f.png)
Izvor: Međunarodna matematička olimpijada, shortlist 1986