I just did something like that recently. The only difference is that I am using two select fields. One select field depends on the value of the other.
Code:
<select class="country">
+---------------+
|Philippines |
+---------------+
<select class="city">
+---------------+
|Cebu City |
+---------------+
I did it using PHP and AJAX(JQuery). I think it would be easy to change it so that it'll observe a radio button instead.
Code:
$(document).ready(function() {
$('select.country').change(function(){
$.get('world/get_city/' + $(this).val(), null,
function(data, textStatus) {
$('select.city').clear;
$('select.city').html(data);
}
);
});
});