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circumcenter of BJK lies on line AC, median, right angle, circumcircle related

Source: 2019 RMM Shortlist G1

June 18, 2020
geometrycircumcircleCircumcentermedian

Problem Statement

Let BMBM be a median in an acute-angled triangle ABCABC. A point KK is chosen on the line through CC tangent to the circumcircle of △BMC\vartriangle BMC so that ∠KBC=90∘\angle KBC = 90^\circ. The segments AKAK and BMBM meet at JJ. Prove that the circumcenter of △BJK\triangle BJK lies on the line ACAC.
Aleksandr Kuznetsov, Russia
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