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# Perl, 147 bytes

Reads list of points from stdin. Prints chosen point.

```
perl -ple'@P=/\d+/g;($c,$a,$b)=map{$p=($_+2)%6;($P[$_]-$P[$p])**2+($P[$_+1]-$P[$p+1])**2}0,2,4;$p=$c>$b?$b>$a?0:2:$c>$a?0:4;$_=join",",@P[$p,$p+1]'
```

Comments:
```
perl -ple'
    # load input
    @P=/\d+/g;

    # compute distances
    ($c,$a,$b) = map {
        $p = ($_+2)%6;
        ($P[$_]-$P[$p])**2 + ($P[$_+1]-$P[$p+1])**2
    } 0,2,4;

    # choose appropriate index into point list
    $p = $c>$b
         ? $b>$a ? 0 : 2
         : $c>$a ? 0 : 4
       ;

    # display
    say join ",", @P[$p,$p+1]
'
```

[Try it online!][TIO-mml86uw4]

[TIO-mml86uw4]: https://tio.run/##XVPbbhpBDH33V6zoRgrBKDv3mUUk@YS8NxGClLRUKayAt9JfL/XxoAj1ZTw@vhz7zO6w3n@E85fmfbdvjuvDsfmx3G/XhwMN@832@N6Mbg7N9KEZcbuYnZ@e5/cv3yb332e37Ru3S25X4/mv5fC7Hea37WJixzdRQs9f28XrFGZ4Hd/d2UmFJuYCygXwn44t@5nUtm8P7eqxXT20y8eutz183CS4mP/cbbYjHvETSlmrz2fHrpk1ho2cTs6@AXJS5ASErjMs2/8yBCF3qXZXGbXaXTLMZwx5yBCEnPrX3HKnon7mIGdgL2jRKZCbOH3myp2iZnmNFeHoGyAnRU5AhLloN2REufe4C0dWPylHUY5MIqJyBJ0qKUeQ3KhZ6WqeeEGjzloUlTslZbPaoSohiEyZNctcTZkph9rCqzYlsMEccCmwxSTOamHy7CNawZKL7HKVESyuq0G4FDt2KCwytw4tWyGolkxij/Gc9IEctuPYoRQ@Gc@mq6Rqk@ikrLCUOYLUirwI5swJO6slK@1tLYlRtcuuVsZIwXDEoKXjgNki1OjVUJYPV3fJXLSB4xzQFjg5eTuIbgxbkJrCAY@iOGXHXvuK7koakd1XSyJnKBcJ9eHkHbCr4lDC1Y8apw/oXz9J4dJuqbDFRNkzRFAY0uvHVKqOUpewCmARKGgveXv9UXKNAaaU2AL0vj6dNFVC9UmUCPrMsghaxMQZ2qpPcuqa1uKdZSFXlVec/u6G42a3PZynw8c/ "Perl 5 – Try It Online"