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<BAC = 2 <ABC wanted, AC + AI = BC given , incenter I

Source: 2020 Dutch IMO TST 1.1

November 21, 2020
geometryincenterequal angles

Problem Statement

In acute-angled triangle ABC,IABC, I is the center of the inscribed circle and holds ∣AC∣+∣AI∣=∣BC∣| AC | + | AI | = | BC |. Prove that ∠BAC=2∠ABC\angle BAC = 2 \angle ABC.
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