I found a class that relies on a method that is defined in an extension of it. Is this a pattern?

I found a class that looks something like:

using System;
// no using statement that brings either IMyClass or
// MyClassExtensions into scope

namespace Org.Foo {

    class MyClass {

    public void QuizzicalMethod(IMyClass thingy,
                                string stringToPass) {
        thingy.ExtensionMethod(StringToPass);
    }
}

There is an IMyClass interface definition in IMyClass.cs in the codebase (in the same namespace and directory), but it contains no definition for QuizzicalMethod. Instead, MyClassExtensions.cs has:

using System;
namespace Org.Foo {
    public static class MyClassExtensions {
        public static void ExtensionMethod (this IMyClass self,
                                            string stringToPass) {
            // Do some stuff
        }
    }
}

Thus, MyClassExtensions is clearly out of scope when MyClass is defined, and thus when QuizzicalMethod--which uses IMyClassExtensions.ExtensionMethod--is defined. It seems to me like both the parameter list of the QuizzicalMethod definition and its call of thingy.ExtensionMethod ought to break. (Makes me wonder if there's a code coverage issue in the tests.) This leads to some questions:

• How does this compile without an error?
• Why would a class author even want to bring QuizzicalMethod out of the class definition and put it into an extension?
• Does this fit an existing named pattern?
• Is there some kind of scoping exception or late-binding going on? If so, how does it not break everything else in C#?

Thanks in advance!

EDIT: Fixed some typos.