**Core Concept**
Ligation of the internal iliac artery is a surgical procedure that involves cutting and tying off the internal iliac artery, a major vessel that supplies blood to the pelvic region. This procedure is often performed to control bleeding during pelvic surgery or to treat conditions such as pelvic fractures.

**Why the Correct Answer is Right**
Ligation of the internal iliac artery leads to ischemia of the pelvic organs, including the bladder, rectum, and reproductive organs. The internal iliac artery gives off several branches, including the superior gluteal artery, which supplies the gluteus maximus muscle, and the inferior gluteal artery, which supplies the gluteus maximus muscle. Ligation of the internal iliac artery also affects the internal pudendal artery, which supplies the external genitalia.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because ligation of the internal iliac artery does not directly affect the femoral artery, which is a separate vessel that supplies the lower extremities.
* **Option B:** This option is incorrect because ligation of the internal iliac artery does not directly affect the renal artery, which is a separate vessel that supplies the kidneys.
* **Option C:** This option is incorrect because ligation of the internal iliac artery does not directly affect the common iliac artery, which is a separate vessel that supplies the lower extremities.

**Clinical Pearl / High-Yield Fact**
It is essential to note that ligation of the internal iliac artery can lead to complications such as ischemic necrosis of the pelvic organs, and therefore, it should be performed with caution and under close monitoring.

**Correct Answer: A.**