radio button is checked but display not check

In the WordPress back-end you have to use checked="checked" (stricter XHTML), because the CSS will not be applied otherwise:

<input type="radio" name="colors" id="blue" checked="checked">

this is the CSS that applies the blue dot:

enter image description here

WordPress already provides a function for this checked()

<input type="radio" name="colors" id="blue" <?php checked( 'red', get_option( 'color' ) ); ?> />

so you dont have to do an If and echo.