Trying to download string and can't search in it context

Question

I am using WebClient to download string html from WebSite and then i am trying to manipulate the string by using SubString and IndexOf..

Also some times i use the functions: substring, indexOf or contains and a strange thing happens: Some times it shows a text (HTML code) and some times it isn't show anything at all.

using (WebClient client = new WebClient())
        {
            htmlCode = client.DownloadString("https://www.google.com");
        }

This is my code for getting an html code from a web site. Now for example in this site i want to get the source of an image - a specific img (or another attribute)

using (StringReader reader = new StringReader(htmlCode))
        {
            string inputLine;
            while ((inputLine = reader.ReadLine()) != null)
            {
                if (inputLine.Contains("img"))
                {
                   RichTextBox.Text += inputLine;
                }
             }
        }

There May be some syntax problems but don't look at it, They are not important.

Do you have an alterenetive or better way to get an HTML source code from a page and handle with it. It has to be HTTPS site and i would like a good explanation of it.

Sorry for noob question.