The construction "Despite X, Y occurred" indicates that Y happened notwithstanding the obstacle X.
"Despite his injuries" suggests that completing the race would be arduous or improbable.
A word is required to express the achievement of a difficult task.
Analysis of options:
- (a) succeeded to finish the race: The phrasing "succeeded to finish" is syntactically awkward; "succeeded in finishing" or "succeeded and finished" are more idiomatic. While it denotes accomplishment, "managed to" is a more common alternative.
- (b) managed to finish the race: "Managed to" signifies successfully completing something that presented difficulty or a challenge, aligning perfectly with overcoming injuries to finish a race.
- (c) failed to finish the race: This option is contradictory to the "despite" clause if the intent is to illustrate perseverance. "Despite his injuries, he failed" implies the injuries were insurmountable, which is a possibility. However, "managed" or "succeeded" better reflect overcoming an impediment. The phrase "failed to finish" is grammatically sound.
- (d) paused to finish the race: "Paused to finish" lacks logical coherence in this context. Pausing occurs during a race, not as a means to complete it. "Paused before finishing" or "paused then finished" might be sensible, but not "paused to finish".
Comparison of (a), (b), and (c):
"Despite his injuries" implies an effort to overcome them.
- "managed to finish" highlights the difficulty and the successful endeavor.
- "succeeded to finish" is less natural than "managed to finish" or "succeeded in finishing".
- "failed to finish" indicates that the injuries prevented completion. While grammatically correct, "managed to finish" generally conveys a stronger sense of overcoming the specific challenge mentioned.
The idiom "managed to do something" is frequently employed to denote accomplishment against adversity.
Example: "Despite the storm, the pilot managed to land the plane safely."
In this scenario, "managed" implies successful completion against the odds. If the athlete completed the race, "managed to finish" is highly appropriate. If the athlete did not complete the race, "failed to finish" would be suitable.
Given that "despite" typically introduces a concession against which a positive outcome is achieved, "managed" is the most fitting choice.
\[ \boxed{\text{managed}} \]