**Core Concept**
Medullary thyroid carcinoma (MTC) is a type of thyroid cancer that originates from the parafollicular cells, also known as C cells. These cells are responsible for producing calcitonin, a hormone involved in calcium homeostasis. MTC is often associated with genetic mutations, particularly in the RET proto-oncogene.

**Why the Correct Answer is Right**
The treatment of choice for medullary thyroid carcinoma involves a combination of surgical and medical management. Specifically, the primary treatment for MTC is **surgical resection**, which aims to remove the tumor and affected thyroid gland. This is often followed by **calcitonin-level monitoring** to detect any recurrence or metastasis. In some cases, **thyroidectomy** or **near-total thyroidectomy** may be necessary to ensure complete removal of the tumor.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because MTC is not typically treated with radioactive iodine (RAI) therapy, which is more commonly used for other types of thyroid cancer that arise from follicular cells.
**Option B:** This option is incorrect because chemotherapy is not the primary treatment for MTC, although it may be used in some cases of advanced or metastatic disease.
**Option C:** This option is incorrect because external beam radiation therapy is not typically used as a primary treatment for MTC.

**Clinical Pearl / High-Yield Fact**
It's essential to note that medullary thyroid carcinoma can be associated with multiple endocrine neoplasia (MEN) syndromes, particularly MEN 2A and MEN 2B. These syndromes are characterized by the presence of other endocrine tumors, such as pheochromocytoma and hyperparathyroidism.

**Correct Answer:** C. Surgical resection is the primary treatment for medullary thyroid carcinoma.