设计继承二叉树类的二叉搜索树类

我正在c#中创建一个二叉搜索树类。我创建这个类是从一个二叉树类派生出来的因为二叉搜索树也是一种二叉树。因此，我将在二叉树类中使用大多数常用方法，并在二叉搜索树中共享它们。

:BinaryTree类有两个方法"addtolleft"answers"AddToRight"方法，这两个方法必须能够访问类外，即在Main方法中添加节点到二叉树。所以我把它们公开了。这两个方法也应该可以在二叉搜索树类中访问(重用)，以便根据条件向二叉搜索树添加节点。

但是现在因为Insert方法是候选的二进制搜索树插入节点到BST，但addtolleft和AddToRight不是。所以这两个方法不应该暴露给BST对象上的二进制搜索树的客户端(外部世界)。如何设计这门课?

I tried:

1. 使这两个方法在binarytree类中密封，它没有帮助。
2. 在base中声明为public，在派生中声明为protected。这也没有帮助，因为public不能作为protected在派生类中继承。

请帮忙设计类。

public class BTNode
{
    public int data;
    public BTNode Left { get; set; }
    public BTNode Right { get; set; }
    public BTNode(int data)
    {
        this.data = data;
    }
}
public class BinaryTree
{
    public BTNode Root { get; set;}
    public BinaryTree() : this(null) { }
    public BinaryTree(BTNode node) { Root = node; }
    // this method common for its derived class too
    public void AddToLeft(BTNode current, BTNode node) 
    {
        current.Left = node;
    }
    // this method common for its derived class too
    public void AddToRight(BTNode current, BTNode node)
    {
        current.Right = node;
    }
}
public class BinarySearchTree : BinaryTree
{       
    public BinarySearchTree(int val)
    {
        Root = new BTNode(val);    
    }
    public void Insert(int val)
    {
        BTNode node = new BTNode(val);
        if (Root.data >= val)
            base.AddToLeft(Root, node); // I should be able to call this method here
        else
            base.AddToRight(Root, node); // I should be able to call this method here
    }
}
class Program
{
    static void Main(string[] args)
    {
        BinaryTree bt = new BinaryTree();
        BTNode root = new BTNode(3);
        BTNode node1 = new BTNode(4);
        BTNode node2 = new BTNode(7);
        bt.AddToLeft(root,node1); // i should be able to access this method here.
        bt.AddToLeft(root, node2); // i should be able to access this method here.
        BinarySearchTree bst = new BinarySearchTree(6);
        bst.Insert(4);
        bst.Insert(8);
        // This is the problem.
        // these two methods should not be visible on the bst object.
        // insertion to bst is done only through insert() method
        // but these two methods should be accessible inside the binarysearchtree class
        // to add the nodes.
        bst.AddToLeft(root,node1); // i should not access this method here on this object
        bst.AddToRight(root, node2); // i should not access this method here on this object
    }
}