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parallelogram wanted, (BOC) related

Source: - All-Russian MO 1998 Regional (R4) 10.2

September 17, 2024
circumcirclegeometryparallelogram

Problem Statement

In an acute triangle ABCABC, a circle SS is drawn through the center OO of the circumcircle and the vertices BB and CC. Let OKOK be the diameter of the circle SS, DD and EE, be it's intersection points with the straight lines ABAB and ACAC respectively. Prove that ADKEADKE is a parallelogram.
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