1.

<RadioButton

                Content="type 1"

                IsChecked="{Binding Path=MyTypeProperty, Mode=TwoWay, Converter={StaticResource ConvertMyType}, ConverterParameter=type1}" />

           <RadioButton

                Content="type 2"

                IsChecked="{Binding Path=MyTypeProperty, Mode=TwoWay, Converter={StaticResource ConvertMyType}, ConverterParameter=type2}" />

 

Your value converter :

public class ConvertMyType : IValueConverter    {        #region Methods        public object Convert(object value, Type targetType, object parameter, System.Globalization.CultureInfo culture)        {            if (value == null || parameter == null)                return value;            return value.ToString().Equals(parameter.ToString());        }        public object ConvertBack(object value, Type targetType, object parameter, System.Globalization.CultureInfo culture)        {            if (value == null || parameter == null)                return value;            return parameter;        }        #endregion Methods    }2