wget ssl alert handshake failure

It works from here with same OpenSSL version, but a newer version of wget (1.15). Looking at the Changelog there is the following significant change regarding your problem:

1.14: Add support for TLS Server Name Indication.

Note that this site does not require SNI. But www.coursera.org requires it. And if you would call wget with -v --debug (as I've explicitly recommended in my comment!) you will see:

$ wget https://class.coursera.org
...
HTTP request sent, awaiting response...
  HTTP/1.1 302 Found
...
Location: https://www.coursera.org/ [following]
...
Connecting to www.coursera.org (www.coursera.org)|54.230.46.78|:443... connected.
OpenSSL: error:14077410:SSL routines:SSL23_GET_SERVER_HELLO:sslv3 alert handshake failure
Unable to establish SSL connection.

So the error actually happens with www.coursera.org and the reason is missing support for SNI. You need to upgrade your version of wget.

You probably have an old version of wget. I suggest installing wget using Chocolatey, the package manager for Windows. This should give you a more recent version (if not the latest).

Run this command after having installed Chocolatey (as Administrator):

choco install wget