Every page is a URL.
You will use the header() function on the page that your form is submitting to, if it's the same page then you need to block out the header function for people who are just arriving to this page.
Something like:
<?php
if (isset($radio_choice)) {
switch($radio_choice) {
case 1:
$location = "my_other_page.php";
break;
case 2:
$location = "yet_another_page.php";
break;
default:
$location = $PHP_SELF;
break;
}
header("Location: $location");
}