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<ACB=60 iffAE + BD = AB, angle bisectors (2016 Kyiv City MO 8.5)

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September 5, 2020
geometryangle bisectorangles

Problem Statement

In the triangle ABCABC the angle bisectors ADAD and BEBE are drawn. Prove that ∠ACB=60∘\angle ACB = 60 {} ^ \circ if and only if AE+BD=ABAE + BD = AB.
(Hilko Danilo)
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