Problem

Source: 2022 Turkey JBMO TST P7 + 2023 Dutch BxMO TST, Problem 4

Tags: geometry, circumcircle



In a triangle ABC with ABC<BCA, we define K as the excenter with respect to A. The lines AK and BC intersect in a point D. Let E be the circumcenter of BKC. Prove that 1|KA|=1|KD|+1|KE|.