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|.
Problem
Source: 2022 Turkey JBMO TST P7 + 2023 Dutch BxMO TST, Problem 4
Tags: geometry, circumcircle