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present participle adjective from fight (v.). Fighting chance is from 1877; fighting mad is attested by 1750.
Old English feohtan "to fight" (class III strong verb; past tense feaht, past participle fohten), from Proto-Germanic *fekhtanan (cf. Old High German fehtan, German fechten, Middle Dutch and Dutch vechten, Old Frisian fiuhta "to fight"), from PIE *pek- "to pluck out" (wool or hair), apparently with a notion of "pulling roughly" (cf. Greek pekein "to comb, shear," pekos "fleece, wool;" Persian pashm "wool, down," Latin pectere "to comb," Sanskrit paksman- "eyebrows, hair").
Spelling substitution of -gh- for a "hard H" sound was a Middle English scribal habit, especially before -t-. In some late Old English examples, the middle consonant was represented by a yogh. To fight back "resist" is recorded from 1890.
Old English feohte, gefeoht "a fight;" see fight (v.). Cf. Old Frisian fiucht, Old Saxon fehta, Dutch gevecht, Old High German gifeht, German Gefecht.