Famous from 《史记·项羽本纪》 in the Hongmen Banquet scene: 樊哙 burst in 瞋目视项王,头发上指,目眦尽裂 — 'glaring at King Xiang, his hair standing on end, his eye-sockets bursting.' The four-character phrase 目眦尽裂 became the canonical image of fury.
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Literary and classical. In modern speech, 眼角 (yǎnjiǎo, corner of the eye) or just 眼眶 (yǎnkuàng, eye socket) are normal; 目眦 mainly survives in set phrases.