Php newbie, how to get php variable from new html form

hello I'm trying to use a form to post variables from an index.html to an action_page.php then somehow get those variables from a new results.html page (is this possible to do?)

my index form looks like this

<form action="action_page.php" method="post">
<select name="race" style="width: 180px;">
<option value="White">White</option>
<option value="Asian">Asian</option> // 
</select>

my php looks like this

<?php
if(isset($_POST["formSubmit"]) )
{
  $varRace = $_POST["race"];
  $varAge = $_POST["age"];

echo $varRace; // this doesn't work why?

}

function redirect($url, $statusCode = 303)
{
header('location: ' .$url, true, $statusCode);
die();
}
$varRedirect = "results.html";
// call to function removed but it would call redirect($varRedirect);
?>

ultimately i'd like my results.html page to display a variable $varRace for instance.

since forms post to themselves is this possible to get ? is there a php function I could write to send the variable?