为什么javascript+CSS显示设置会使单选按钮不受欢迎

我有一个简单的javascript，它可以根据下拉菜单选项隐藏/显示各种div，但它会使其中一个div上的单选按钮消失。。。有人知道为什么吗？带有单选按钮的列表是程序化的，它可以使用"书本"选项，但不能使用"视频"选项。代码：

<script>
    function showstuff(boxid){
        if(boxid=="Book" || boxid=="Layers" || boxid=="3D"){
            document.getElementById("Video").style.display="none";
            document.getElementById("Book").style.display="inline";
        }else{
            document.getElementById("Video").style.display="inline";
            document.getElementById("Book").style.display="none";
        }
    }
</script>
 <select id="ARtype" name="ARtype" onChange="showstuff(this.value)">
    <option selected="selected" value="Book">Book</option>
    <option value="Video">Video</option>
    <option value="Layers">Layers</option>
    <option value="3D">3D</option>
</select>
        <div id="Video" style="display:none;">
    <dl><a href="uploadvideo.php">Upload Video</b>
            <img src="images/upload2.png" alt="Upload assets" /></a><br>
         <dt><label for="video">Video Overlay*</label></dt>     
        <!-- ###GET IMAGES FROM TRIGGERS FOLDER -->
    </dl>
        <table><tr><td>
        <?php
        foreach (glob("cmpping/videos/*.*") as $myimage){
           echo "<div style='"float:left;border-right:1px solid black;padding-right:5px;margin-left:5px;''"><span style='"white-space:nowrap;padding-bottom:0px;line-height:30px;'">
                    <input name='"URLVideo'" id='"URLVideo'" type='"radio'" value='"$myimage'"/>
                    <img align='"middle'" width='"30'" style='"max-height:50px;margin-left:5px;'" src='"img/video.png'" /><br>".str_replace("cmpping/videos/","",$myimage) ."</span></div> ";
        }
        ?>
        </td></tr></table>
        <table><tr><td>
        <?php
        foreach (glob("cmpping/trigger/*.*") as $myimage){
            echo "<!--triggerimage=" . $query_result->triggerimage . "--><!--myimage=".$myimage ."-->";
            echo "<span style='"white-space:nowrap;padding-bottom:20px;line-height:70px;'">
                    <input name='"triggerid'" id='"triggerid'" type='"radio'" value='"$myimage'"/>
                    <img align='"middle'" width='"50'" style='"max-height:50px;margin-left:5px;'" src='"$myimage'" /></span> ";
        }
        ?>
        <!--<input type="file" name="triggerid" id="triggerid" r />--> 
        </td></tr></table>
</div>
<div id="Book" style="display: inline">
        <table><tr><td>
        <?php
        foreach (glob("cmpping/trigger/*.*") as $myimage){
            echo "<!--triggerimage=" . $query_result->triggerimage . "--><!--myimage=".$myimage ."-->";
            echo "<span style='"white-space:nowrap;padding-bottom:20px;line-height:70px;'">
                    <input name='"triggerid'" id='"triggerid'" type='"radio'" value='"$myimage'"/>
                    <img align='"middle'" width='"50'" style='"max-height:50px;margin-left:5px;'" src='"$myimage'" /></span> ";
        }
        ?>
        <!--<input type="file" name="triggerid" id="triggerid" r />--> 
        </td></tr></table>
</div>