The correct answers are A) foreign relations and B) power to declare war.
Some of the important national security responsibilities the president shares with Congress are foreign relations and power to declare war.
The Powers of the President that are shared with Congress are foreign relations, the appointment of Ambassadors, make treaties, and to approve legislation. The President cannot declare war, for that to happen it needs the authorization of Congress, although the President can send troops to any country. Some of the Presidential powers detailed in Article II of the US Constitution are to serve as the Commander in Chief of the Armed Forces, Convene Congress in special sessions, to lead the executive branch and the Cabinet, and appoint Supreme Court Justices.