Single SSL proxy to multiple SSL and non-SSL domain names

After some puzzeling I found the way to create a SSL web proxy that connects to SSL and non-SSL websites. This is an example of the VirtualHost configuration in the ssl.conf file.
Read more about creating ssl websites here.

NameVirtualHost *:443

<VirtualHost *:443>
    ServerName site_no_ssl.r71.nl
    SSLEngine On

    SSLCertificateFile /etc/pki/tls/certs/localhost.crt
    SSLCertificateKeyFile /etc/pki/tls/private/localhost.key

    ProxyPass / http://site_no_ssl.r71.nl/centreon/
    ProxyPassReverse / http://site_no_ssl.r71.nl/centreon/
</VirtualHost>

<VirtualHost *:443>
    ServerName other_site_no_ssl.r71.nl
    SSLEngine On

    SSLCertificateFile /etc/pki/tls/certs/localhost.crt
    SSLCertificateKeyFile /etc/pki/tls/private/localhost.key

    ProxyPass / http://other_site_no_ssl.r71.nl/
    ProxyPassReverse / http://other_site_no_ssl.r71.nl/
</VirtualHost>

<VirtualHost *:443>
    ServerName site_with_ssl.r71.nl

    <Proxy *>
        Order deny,allow
        Allow from all
    </Proxy>

    SSLEngine on
    SSLProxyEngine On
    SSLCertificateFile /etc/pki/tls/certs/localhost.crt
    SSLCertificateKeyFile /etc/pki/tls/private/localhost.key

    ProxyRequests On
    ProxyPreserveHost On
    ProxyPass / https://site_with_ssl.r71.nl:443/
    ProxyPassReverse / https://site_with_ssl.r71.nl:443/
</VirtualHost>