We have online shopping site. When I am going to checkout page i am getting a error like this "error:14094410:SSL routines:SSL3_READ_BYTES:sslv3 alert handshake failure(35)"

From the apache error log i can see some attempts to connect to api.paypal.com. Here is the part of my apache error log

* About to connect() to api.paypal.com port 443 (#0)
*   Trying 66.211.168.123... * connected
* Connected to api.paypal.com (66.211.168.123) port 443 (#0)
* successfully set certificate verify locations:
*   CAfile: none
  CApath: /etc/ssl/certs
* error:14094410:SSL routines:SSL3_READ_BYTES:sslv3 alert handshake failure
* Closing connection #0

When i tried to connect to api.paypal.com using curl i am getting a error like this

curl -iv https://api.paypal.com/
* About to connect() to api.paypal.com port 443 (#0)
*   Trying 66.211.168.91... connected
* Connected to api.paypal.com (66.211.168.91) port 443 (#0)
* successfully set certificate verify locations:
*   CAfile: none
  CApath: /etc/ssl/certs
* SSLv3, TLS handshake, Client hello (1):
* SSLv3, TLS handshake, Server hello (2):
* SSLv3, TLS handshake, CERT (11):
* SSLv3, TLS handshake, Request CERT (13):
* SSLv3, TLS handshake, Server finished (14):
* SSLv3, TLS handshake, CERT (11):
* SSLv3, TLS handshake, Client key exchange (16):
* SSLv3, TLS change cipher, Client hello (1):
* SSLv3, TLS handshake, Finished (20):
* SSLv3, TLS alert, Server hello (2):
* error:14094410:SSL routines:SSL3_READ_BYTES:sslv3 alert handshake failure
* Closing connection #0
curl: (35) error:14094410:SSL routines:SSL3_READ_BYTES:sslv3 alert handshake failure

Can anyone help me to figure out this.

Thanks in Advance. Arun S