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angle condition with Lemoine point

Source: 2023 Viet Nam math olympiad for high school students D1 P10

March 25, 2023
geometry

Problem Statement

Given a triangle ABCABC with Lemoine point L.L. Choose points X,Y,ZX,Y,Z on the segments LA,LB,LC,LA,LB,LC, respectively such that:∠XBA=∠YAB,∠XCA=∠ZAC.\angle XBA=\angle YAB,\angle XCA=\angle ZAC. Prove that: ∠ZBC=∠YCB.\angle ZBC=\angle YCB.
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