**Core Concept**
The Hesselbach's triangle and femoral triangle are anatomical regions in the anterior abdominal wall and thigh, respectively. These triangles are clinically significant due to the presence of vital structures that can be compromised during various procedures or injuries.

**Why the Correct Answer is Right**
The correct answer is a common structure found in both triangles. This structure is the **femoral artery** in the femoral triangle and the **superficial inferior epigastric artery** in the Hesselbach's triangle. Both arteries run within the boundaries of these triangles and play crucial roles in supplying blood to the surrounding tissues. The femoral artery is a continuation of the external iliac artery and passes through the femoral triangle, while the superficial inferior epigastric artery arises from the femoral artery and enters the Hesselbach's triangle.

**Why Each Wrong Option is Incorrect**
* **Option A:** The femoral vein is also present in the femoral triangle but is not the common structure being referred to in this context.
* **Option B:** The femoral nerve is located lateral to the femoral artery in the femoral triangle and does not have a direct counterpart in the Hesselbach's triangle.
* **Option C:** The inguinal ligament forms the base of both triangles but is not a structure that is commonly found within them.

**Clinical Pearl / High-Yield Fact**
When performing surgical procedures or administering injections in these regions, it is essential to identify and avoid damaging the femoral artery and its branches to prevent complications such as hemorrhage.

**Correct Answer:** C.