The words piqued, peaked, peeked sound the same but have different meanings and spellings. Why do piqued, peaked, peeked sound the same even though they are completely different words?
The answer is simple: piqued, peaked, peeked are homophones of the English language.
Ending in a peak; pointed: a peaked cap.
Having a sickly appearance: You're looking a little peaked today.
Simple past tense and past participle of peek.
Simple past tense and past participle of pique.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition, from Wiktionary, Creative Commons Attribution/Share-Alike License and Wordnik.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.