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Making a triangle with 3 segments

Source: 239 2019 J3

July 31, 2020
geometry

Problem Statement

Circle ω\omega touches the side ACAC of the equilateral triangle ABCABC at point DD, and its circumcircle at the point EE lying on the arc \overarc{BC}. Prove that with segments ADAD, BEBE and CDCD, you can form a triangle, in which the difference of two of its angles is 60∘60^{\circ}.
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