Client authentication (certificat + private key) using WinHttp - c++

Question

I'm trying to communicate in https with a server using the Win32 API.
Here is a very minimalist code :
HINTERNET ses = WinHttpOpen(L"test",WINHTTP_ACCESS_TYPE_DEFAULT_PROXY,WINHTTP_NO_PROXY_NAME,WINHTTP_NO_PROXY_BYPASS,0 ) ;
HINTERNET con = WinHttpConnect(ses,L"stackoverflow.com",INTERNET_DEFAULT_HTTPS_PORT,0 ) ;
HINTERNET req = WinHttpOpenRequest(con,L"GET",NULL,NULL,WINHTTP_NO_REFERER,WINHTTP_DEFAULT_ACCEPT_TYPES,WINHTTP_FLAG_SECURE ) ;
WinHttpSendRequest( req,WINHTTP_NO_ADDITIONAL_HEADERS,0,WINHTTP_NO_REQUEST_DATA,0,0,0 ) ;
WinHttpReceiveResponse( req,NULL ) ;
char buffer [10000] ;
unsigned long size ;
WinHttpReadData( req,reinterpret_cast<void*>( buffer ),sizeof( buffer )-1,&size ) ;
buffer[size] = 0 ;
cout << buffer << endl ;
As long as I communicate with a "classic" https server like stackoverflow.com everything goes well.
The problem is when I try to communicate with a server that requests an authentication of the client.
I have 3 .pem files : a certificate and a private key for my client, and a root certificate that authenticates my client certificate (i.e. a certificate chain of length 2).
For information, I can connect my server using this cULR command line :
curl https://my.server --cert Client_cert.pem --key Client_key.pem --cacert Root_cert.pem
So I kown it's possible!
Reading the win32 API documentation, I figured out that the key is to call
WinHttpSetOption but it's not clear between the options WINHTTP_OPTION_CLIENT_CERT_CONTEXT and WINHTTP_OPTION_CLIENT_CERT_ISSUER_LIST...
And I did not find out how to pass my data (cert+key files).
Any wise advice ?
Thanks in advance !