Hide/show radio buttons stop working on save

Here's my case: I'm developing a little widget, and I was looking for a way to hide/show different DIVs on selecting a set of radio buttons. I found the proper code and adjusted it to my needs. The only problem is that the hide/show feature stops working after clicking on save while configuring the widget :S

Here's the JS:

jQuery(document).ready(function($) {
    $(document).ready(function() {
        $('input[type="radio"]').click(function(){
            if($(this).attr("value")=="link_to_image"){
                $(".radio-option").hide();
                $(".linked-image").show();
            }
            if($(this).attr("value")=="link_to_page"){
                $(".radio-option").hide();
                $(".linked-page").show();
            }
        });
    });
});

And the HTML:

<p>
    <label>Link:</label><br>
    <label>
        <input type="radio" name="link_to" value="link_to_image">
        Link to image
    </label><br>
    <label>
        <input type="radio" name="link_to" value="link_to_page">
        Link to page
    </label>
</p>
<div class="linked-image radio-option">
    <label for="linked_image">Linked image:</label>
    <p>
        Content for linked_image DIV
    </p>
</div>
<div class="linked-page radio-option">
    <label for="linked_page">Linked page:</label>   
    <p>
        Content for linked_page DIV
    </p>
</div>

And the [JSFiddle] (http://ift.tt/1Doewqc)

Could you give me a hand with this, guys?