What is the term for a bluish discoloration around the mouth?

The term for a bluish discoloration around the mouth is circumoral cyanosis. This condition occurs when there is a lack of oxygen in the blood, causing the skin and mucous membranes to appear bluish. The area around the mouth is particularly affected, which can be indicative of respiratory or circulatory issues that impede adequate oxygen delivery to tissues. Circumoral cyanosis is often observed in conditions such as hypoxia, respiratory depression, or congenital heart defects, and serves as a critical clinical sign that prompts further assessment of the patient's oxygenation status.

The other terms listed relate to different conditions: epistaxis refers to nosebleeds, hemoptysis is the coughing up of blood, and exsanguination indicates severe blood loss. While these terms are medical in nature, they do not pertain to the bluish discoloration of the skin and therefore are not relevant to the question.