Okay, let's tackle this question. The patient has a posterior duodenal ulcer that's actively bleeding, and we need to identify the responsible vessel. First, I remember that duodenal ulcers are commonly associated with the posterior wall, and the main arteries in the duodenum are the gastroduodenal artery and its branches. The posterior duodenal ulcer typically involves the posterior superior pancreaticoduodenal artery, which is a branch of the gastroduodenal artery. Wait, but sometimes the arteries can be a bit confusing. Let me think: the gastroduodenal artery splits into the anterior and posterior branches, and the posterior one is the posterior superior pancreaticoduodenal artery. So in a posterior duodenal ulcer, this artery is likely the one bleeding. The other options might be other arteries like the right gastric artery (which is more for gastric ulcers) or the left gastric artery, but those are in different locations. Also, the common hepatic artery is a bigger vessel and not directly involved in the duodenal wall. So the correct answer should be the posterior superior pancreaticoduodenal artery.

**Core Concept**
Posterior duodenal ulcers commonly bleed due to erosion of the **posterior superior pancreaticoduodenal artery**, a branch of the gastroduodenal artery. This vessel runs along the posterior duodenal wall, making it vulnerable to ulceration.

**Why the Correct Answer is Right**
The posterior superior pancreaticoduodenal artery (PSPDA) is the most common vessel affected in posterior duodenal ulcers. It arises from the gastroduodenal artery and runs posteriorly along the second part of the duodenum. Active bleeding occurs when the ulcer erodes into this artery, leading to brisk, life-threatening hemorrhage. Immediate endoscopic intervention or surgery is often required.

**Why Each Wrong Option is Incorrect**
**Option A:** The *right gastric artery* supplies the lesser curvature of the stomach, not the duodenum.
**Option B:** The *left gastric artery* is responsible for gastric body/upper lesser curvature ulcers, not duodenal.
**Option C:** The *common hepatic artery* is a major branch of the celiac trunk and does not directly supply the duodenal wall.

**Clinical Pearl**
Remember the "rule of 2s" for duodenal ulcers: 2 cm in diameter, 2 cm distal to pylorus, and 2nd part of the duodenum. Posterior ulcers are more likely to bleed than anterior ones due to the PSPDA’s location.

**Correct Answer: C. Posterior superior pancreaticoduodenal artery**

✓ Correct Answer: A. Gastroduodenal aery