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An isogonal conjugate problem

Source: German Bundeswettbewerb 2022, Round 2, Problem 3

September 14, 2022
geometryperpendicular bisector

Problem Statement

In an acute triangle ABCABC with AC<BCAC<BC, lines mam_a and mbm_b are the perpendicular bisectors of sides BCBC and ACAC, respectively. Further, let McM_c be the midpoint of side ABAB. The Median CMcCM_c intersects mam_a in point SaS_a and mbm_b in point SbS_b; the lines ASbAS_b und BSaBS_a intersect in point KK. Prove: ∠ACMc=∠KCB\angle ACM_c = \angle KCB.
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