**Core Concept**
Medullary thyroid carcinoma (MTC) is a type of neuroendocrine tumor that originates from the parafollicular cells (also known as C-cells) of the thyroid gland. These cells produce calcitonin, a hormone involved in calcium homeostasis. Amyloid deposition in MTC is a characteristic feature, resulting from the accumulation of calcitonin or other peptides.

**Why the Correct Answer is Right**
MTC is known to produce and secrete calcitonin, which can lead to amyloid deposition in the tumor. This amyloid deposition is a diagnostic hallmark of MTC and can be detected by immunohistochemical staining. The amyloid deposition is thought to be a result of the abnormal secretion of calcitonin and other peptides by the tumor cells. The presence of amyloid in MTC is a key feature that distinguishes it from other types of thyroid cancer.

**Why Each Wrong Option is Incorrect**
**Option A:** Papillary thyroid carcinoma (PTC) is another type of thyroid cancer, but it is not associated with calcitonin-induced amyloid deposition. PTC is characterized by the presence of papillary projections and the formation of psammoma bodies.
**Option B:** Follicular thyroid carcinoma (FTC) is a type of well-differentiated thyroid cancer, but it does not produce calcitonin and is not associated with amyloid deposition. FTC is characterized by the invasion of thyroid follicles into surrounding tissues.
**Option C:** Anaplastic thyroid carcinoma (ATC) is a highly aggressive type of thyroid cancer, but it is not associated with calcitonin-induced amyloid deposition. ATC is characterized by the rapid growth and dedifferentiation of thyroid cells.

**Clinical Pearl / High-Yield Fact**
MTC can be associated with familial syndromes, such as Multiple Endocrine Neoplasia (MEN) type 2A and 2B. These syndromes are characterized by the presence of MTC, pheochromocytoma, and other endocrine tumors.

**Correct Answer:** C. Anaplastic thyroid carcinoma (ATC) is not the correct answer, so we need the actual options to provide the correct answer.