This is because you are not using ng-model:
FORKED PLUNKER
<div class="radio" ng-repeat="radius in radii" id="selectradius-{{radius.id}}">
  <label>
    <input type="radio" name="radius"
         ng-change="handleRadioClick(selectedRadius)"
         ng-model="radius.checked">
    {{radius.name}}
  </label>
</div>
UPDATE:
I'm sorry that I didn't notice that you wanted to have a default radio button checked, if that is the case then the approach you're taking is incorrect. You must consider the model as non-individual parts in a group of radio buttons but as a whole, they are supposed to be one value instead. You don't have to use ng-repeat's radio scope variable instead use another ng-model as the selectedRadius model. Your input radio needs to have a value, and in this case we'll use ng-value to determine the current value of the model.
UPDATED PLUNKER [2014 September]
JAVASCRIPT
Controller
  $scope.radii = [
    {id:.25, name:"1/4 Mile"},
    {id:.5, name:"1/2 Mile"},
    {id:1, name:"1 Mile"},
    {id:2, name:"2 Mile"},
    {id:3, name:"3 Mile"},
    {id:4, name:"4 Mile"},
    {id:5, name:"5 Mile"}
  ];
  // selected value is {id:2, name:"2 Mile"}
  $scope.selectedRadius = $scope.radii[3];
HTML
<div class="radio" ng-repeat="radius in radii" id="selectradius-{{radius.id}}">
  <label>
    <input type="radio" name="radius"
         ng-change="handleRadioClick(radius)"
         ng-model="selectedRadius"
         ng-value="radius">
    {{radius.name}}
  </label>
</div>
UPDATED PLUNKER [2015 January]
dcz.switcher's problem below suggested that the solution above does not trigger the ng-change event handler when a radio button is reselected. The main problem was that the ng-model was referring to the ng-repeat's scope and not to the controller's scope from the second change. To solve this problem you can use the $parent property. An alternative would be to use controllerAs alias and use the alias itself to access your controller's property. To understand more about scopes in AngularJS, I suggest you read more about it in here.
HTML
<div class="radio" ng-repeat="radius in radii" id="selectradius-{{radius.id}}">
  <label>
    <input type="radio" name="radius"
         ng-change="handleRadioClick($parent.selectedRadius)"
         ng-model="$parent.selectedRadius"
         ng-value="radius">
    {{radius.name}}
  </label>
</div>