**Core Concept**
The external iliac artery is a major blood vessel that runs along the pelvic sidewall, supplying blood to the lower extremities. A hematoma adjacent to this artery suggests that the surrounding tissue or the artery itself may have been damaged.

**Why the Correct Answer is Right**
The external iliac artery is at risk during tubal ligation procedures due to its proximity to the pelvic structures being operated on. A hematoma adjacent to the external iliac artery suggests that the artery may have been injured, leading to bleeding and subsequent hypovolemic shock. The external iliac artery is a common site for injury during pelvic surgeries due to its location and the fact that it is often surrounded by loose areolar tissue that can be easily damaged.

**Why Each Wrong Option is Incorrect**
* **Option A:** The common iliac artery is a larger vessel that branches off into the external iliac artery and internal iliac artery. While it is possible for the common iliac artery to be injured, the presence of a hematoma adjacent to the external iliac artery makes this option less likely.
* **Option B:** The internal iliac artery is a smaller vessel that supplies blood to the pelvic viscera and pelvic sidewall. While it is possible for the internal iliac artery to be injured, the location of the hematoma is more consistent with an injury to the external iliac artery.
* **Option D:** The inferior epigastric artery is a smaller vessel that arises from the external iliac artery and supplies blood to the anterior abdominal wall. While it is possible for the inferior epigastric artery to be injured, the presence of a large hematoma adjacent to the external iliac artery makes this option less likely.

**Clinical Pearl / High-Yield Fact**
Tubal ligation procedures can be associated with a high risk of bleeding due to the proximity of the pelvic structures to major blood vessels. Surgeons must take precautions to avoid injury to these vessels, including careful dissection and the use of electrocautery or other hemostatic agents as needed.

**Correct Answer:** C. External iliac artery.