## **Core Concept**
The supinator muscle is innervated by the **posterior interosseous nerve (PIN)**, a branch of the radial nerve. This nerve supplies the muscles in the forearm that are involved in extension and supination.

## **Why the Correct Answer is Right**
The supinator muscle's nerve supply is crucial for its function in forearm supination. The posterior interosseous nerve (PIN), which is a branch of the radial nerve, provides this innervation. This is similar to the innervation of the **extensor digitorum** muscle, which is also supplied by the posterior interosseous nerve. This shared innervation pattern makes the extensor digitorum a correct match.

## **Why Each Wrong Option is Incorrect**
* **Option A:** The **flexor carpi radialis** is innervated by the median nerve, not the posterior interosseous nerve, making it an incorrect match.
* **Option B:** The **brachialis** muscle is primarily innervated by the musculocutaneous nerve, with a small contribution from the radial nerve, but not by the posterior interosseous nerve.
* **Option D:** The **extensor carpi radialis brevis** is indeed innervated by the radial nerve but more specifically by the nerve to extensor carpi radialis brevis which is a branch of radial nerve before it divides into posterior interosseous nerve, making it less directly comparable to the supinator's innervation.

## **Clinical Pearl / High-Yield Fact**
A key clinical point to remember is that the **posterior interosseous nerve (PIN)** can be compressed or injured, leading to a condition known as **PIN syndrome**. This results in weakness of the muscles supplied by the PIN, including the supinator and extensor digitorum, but spares the extensor carpi radialis brevis, which is innervated before the PIN branch.

## **Correct Answer:** C. extensor digitorum.