Avalonia/samples/XamlTestApplicationPcl/RadioButton.paml

<Styles xmlns="https://github.com/perspex">
  <Style Selector="RadioButton">
    <Setter Property="BorderBrush" Value="#ff333333"/>
    <Setter Property="BorderThickness" Value="2"/>
    <Setter Property="Template">
      <ControlTemplate>
        <Grid ColumnDefinitions="Auto,*">
          <Ellipse Stroke="{TemplateBinding BorderBrush}"
                   StrokeThickness="{TemplateBinding BorderThickness}"
                   Width="18"
                   Height="18"
                   VerticalAlignment="Center"/>
          <Ellipse Name="checkMark"
                   Fill="{TemplateBinding BorderBrush}"
                   Width="10"
                   Height="10"
                   Stretch="Uniform"
                   HorizontalAlignment="Center"
                   VerticalAlignment="Center"/>
          <ContentPresenter Name="PART_ContentPresenter"
                            Content="{TemplateBinding Content}"
                            Margin="4,0,0,0"
                            VerticalAlignment="Center"
                            Grid.Column="1"/>
        </Grid>
      </ControlTemplate>
    </Setter>
  </Style>
  <Style Selector="RadioButton /template/ Ellipse#checkMark">
    <Setter Property="IsVisible" Value="False"/>
  </Style>
  <Style Selector="RadioButton:checked /template/ Ellipse#checkMark">
    <Setter Property="IsVisible" Value="True"/>
  </Style>
</Styles>