extjs treenode add radio group as node property

Question

I'd like this effect.

I wouldn't like Take a nap show as a non-leaf node with 10 minutes and 20 minutes show as leaf child nodes of Take a nap node.

I try with code

    children: [{
        text: 'Take a nap <input type="radio" checked/>10 minutes<input type="radio"/>20 minutes',
        leaf: true,
    },{......}]

It can show as my expection. But can not work since the radio button can't be clicked.

And I don't like implement with menu like this:

    var menu1 = new Ext.menu.Menu({
        items: [
        '<b class="menu-title">Choose Time</b>',
        {
            text: '10 minutes',
            checked: true,
            group: 'time'
        }, {
            text: '20 minutes',
            checked: false,
            group: 'time'
        }]
    });

    children: [{
        text: 'Go jogging',
        leaf: true,

        listeners: {
            'click': function(node,event) {

                x = event.browserEvent.clientX;
                y = event.browserEvent.clientY;
                menu1.showAt([x, y]);
            }
        }
    }

Can extjs do this?

Demo In jsfiddle, for convenience.