Select the most appropriate idiom to complete the sentence.

Despite losing the championship match after months of rigorous training, the athlete took the defeat ____ and vowed to return stronger next season.

The correct option to fill in the blank is on the chin.

Explanation:
The sentence describes an athlete who faced a disappointing defeat after months of hard training, but accepted the result bravely without complaining and remained determined to return stronger in the next season.

Let's break down the meanings of all the given options:
- Take (something) on the chin: To accept courageously and endure hardship, defeat, or criticism without complaining or giving up. This fits the context of a dedicated athlete accepting defeat with resilience.
- Off the cuff: Performed or spoken spontaneously without prior thought or preparation.
- In cold blood: Done ruthlessly, intentionally, and without emotion or mercy.
- At arm's length: Maintaining a distance from someone or something to avoid close involvement or intimacy.

Hence, on the chin is the most appropriate idiom to complete the sentence.