The answer is d. The ophthalmic artery is a branch of the internal carotid artery not the external carotid.
Most of the blood supplied to the face and scalp comes from the external carotid artery, which after the carotid bifurcation gives off a series of branches supplying blood to the structures and skin of the anterior neck, face and scalp:
1. Early branches include the superior thyroid artery and lingual artery which supply blood to the thyroid gland, the muscles of the anterior neck and
the tongue and mucous membranes of mouth and gums.
2. Facial artery. This initially follows the inferior border of the mandible then passes upward to supplies most of the muscles and skin of the face from under the chin (submental artery) to the bridge of the nose (angular artery).
3. Occipital artery passes posteriorly to supply blood to the scalp of the back of the head.
Further upward, and within the parotid gland just anterior to the ear, the external carotid divides into the maxillary artery and slightly smaller superficial temporal artery.
4. Maxillary artery runs deep to the neck of the mandible and supplies blood to the deeper structures of the face and via it’s important branch – the middle meningeal artery (which enters the skull via the foramen spinosum) – the superficial meninges. Another branch, the inferior alveolar artery supplies the teeth and, via its terminal branch the mental artery (which exits the mandible through the mental foramen) the skin of the chin.
5. Superficial temporal artery ascends in front of the ear to the temporal area where it supplies the muscles and skin of the fronto-lateral scalp. The superficial temporal artery, of course, may become inflamed in giant Cell arteritis (temporal arteritis).
The exception to the rule that the external carotid artery supplies the face and scalp, is the ophthalmic artery which supplies most of the structures of the orbit but also the nose (ethmoidal branches) , eyelids (medial palpebral arteries) and skin and muscles forehead (supraorbital artery which exits the cranium via the supraorbital foramen). The ophthalmic artery of course a branch of the internal carotid artery.