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circumcenter of ADE lies on segments AC, orthcenter related

Source: 2018 All-Ukrainian Correspondence MO, grades 5-12 p9

April 29, 2021
geometryCircumcenterorthocenterUkraine Correspondence

Problem Statement

Let ABCABC be an acute-angled triangle in which AB<ACAB <AC. On the side BCBC mark a point DD such that AD=ABAD = AB, and on the side ABAB mark a point EE such that the segment DEDE passes through the orthocenter of triangle ABCABC. Prove that the center of the circumcircle of triangle ADEADE lies on the segment ACAC.
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