The left and right common carotid arteries are the two arteries leading to the head and supply the brain with blood and oxygen. Shortly after they split off the highest point of the aorta, each splits into two branches - the left and right external carotid artery and the internal carotic artery. A blockage in one of these arteries leads to a stroke.

The left common carotid travels through the chest before entering the neck. The right common carotid starts in the neck. Because both lie close to the skin, they are useful for checking the pulse of a patient who is unconscious or has no pulse in the extremities.

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Diagram of the branching of the carotid from the aorta. Source: Wikipedia.