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AK_|_ BC wanted, 2 circles related

Source: 2020 Korea Junior Math Olympiad p2 KJMO

November 24, 2021
geometryperpendicular

Problem Statement

Let ABCABC be an acute triangle with circumcircle Ω\Omega and AB‾<AC‾\overline{AB} < \overline{AC}. The angle bisector of AA meets Ω\Omega again at DD, and the line through DD, perpendicular to BCBC meets Ω\Omega again at EE. The circle centered at AA, passing through EE meets the line DEDE again at FF. Let KK be the circumcircle of triangle ADFADF. Prove that AKAK is perpendicular to BCBC.
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