**Core Concept**
Anaplastic thyroid carcinoma (ATC) is a highly aggressive and rare form of thyroid cancer characterized by rapid growth and invasion into surrounding structures, such as the trachea and sternum. The treatment of ATC is often challenging due to its aggressive nature and limited response to conventional therapies.

**Why the Correct Answer is Right**
The treatment of choice for ATC infiltrating the trachea and sternum typically involves a multimodal approach, combining surgery, radiation therapy, and systemic therapy. **External Beam Radiation Therapy (EBRT)** plays a crucial role in controlling local tumor growth and alleviating symptoms. **Option C: Palliative EBRT** is the correct answer because it targets the tumor's local invasion into the trachea and sternum, providing symptom relief and improving quality of life.

**Why Each Wrong Option is Incorrect**
* **Option A:** is incorrect because surgery alone is rarely sufficient for ATC with extensive local invasion, and may even lead to increased morbidity.
* **Option B:** is incorrect because chemotherapy has limited efficacy in ATC and is not the primary treatment modality in this scenario.
* **Option D:** is incorrect because targeted therapy may have some role in ATC, but it is not the primary treatment for locally advanced disease with tracheal and sternal invasion.

**Clinical Pearl / High-Yield Fact**
For patients with ATC, early palliative care integration is essential to manage symptoms, improve quality of life, and address end-of-life concerns.

**Correct Answer: C. Palliative EBRT. Palliative External Beam Radiation Therapy.**