**Core Concept**
The radial nerve is a major branch of the brachial plexus that runs along the humerus, making it susceptible to injury in cases of humeral fractures, particularly those involving the distal shaft. This nerve is responsible for motor innervation of the triceps brachii and extensor muscles of the forearm, as well as sensory innervation of the back of the hand and forearm.

**Why the Correct Answer is Right**
The radial nerve is commonly injured in fractures of the distal shaft of the humerus due to its anatomical course, which places it in close proximity to the bone. As the nerve runs down the radial groove of the humerus, it can become compressed or stretched, leading to nerve damage. This is often seen in fractures that are displaced or comminuted, where the nerve can become trapped between fragments of bone.

**Why Each Wrong Option is Incorrect**
**Option A:** The median nerve is not typically involved in fractures of the distal shaft of the humerus, as it runs along the medial aspect of the arm and is more commonly associated with injuries to the elbow or wrist.

**Option B:** The ulnar nerve is not commonly involved in fractures of the distal shaft of the humerus, as it runs along the medial aspect of the arm and is more commonly associated with injuries to the elbow, particularly cubital tunnel syndrome.

**Option C:** The axillary nerve is not typically involved in fractures of the distal shaft of the humerus, as it arises from the posterior cord of the brachial plexus and is more commonly associated with injuries to the shoulder or axilla.

**Clinical Pearl / High-Yield Fact**
In patients with a suspected radial nerve injury, it is essential to examine for signs of wrist drop, including weakness or paralysis of wrist extension and a positive Tinel's sign over the radial groove.

**Correct Answer:** C. The ulnar nerve is not commonly involved in fractures of the distal shaft of the humerus, as it runs along the medial aspect of the arm and is more commonly associated with injuries to the elbow, particularly cubital tunnel syndrome.