The sentence structure "Despite X, Y happened" implies that Y occurred in the face of adversity X.
"Despite his injuries" sets up an expectation that finishing the race would be difficult or unlikely.
We need a word that conveys accomplishing something difficult.
Let's analyze the options:
- (a) succeeded to finish the race: "Succeeded to finish" is grammatically a bit awkward. "Succeeded in finishing" or "succeeded and finished" would be more natural. While it conveys achievement, the phrasing is less common than "managed to".
- (b) managed to finish the race: "Managed to" implies successfully doing something that was difficult or challenging. This fits perfectly with the context of overcoming injuries to finish a race.
- (c) failed to finish the race: This contradicts the "despite" clause if the intention is to show perseverance. "Despite his injuries, he failed" means the injuries were too severe, which is possible, but "managed" or "succeeded" better reflect overcoming an obstacle. However, the word must fit the blank before "to finish the race". "failed to finish" is a valid phrase.
- (d) paused to finish the race: "Paused to finish" doesn't make logical sense in this context. One pauses during a race, not to finish it. "Paused before finishing" or "paused then finished" might make sense, but not "paused to finish".
Comparing (a), (b), and (c):
"Despite his injuries" suggests an effort to overcome them.
- "managed to finish" emphasizes the difficulty and the successful effort.
- "succeeded to finish" is less idiomatic than "managed to finish" or "succeeded in finishing".
- "failed to finish" means the injuries prevented completion. While grammatically correct, "managed to finish" often carries a stronger sense of overcoming the specific challenge mentioned.
The phrase "managed to do something" is very commonly used to indicate achievement in the face of difficulty.
Example: "Despite the storm, the pilot managed to land the plane safely."
In this context, "managed" implies successful completion against odds. If the athlete finished, "managed to finish" is very appropriate. If the athlete didn't finish, "failed to finish" would be appropriate.
Since "despite" usually introduces a concession against which a positive outcome occurs, "managed" fits best.
\[ \boxed{\text{managed}} \]