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an angle ratio

Source: Mathematics Regional Olympiad of Mexico Southeast 2015 P5

October 26, 2021
geometryangle bisectorratio

Problem Statement

In the triangle ABCABC, let AMAM and CNCN internal bisectors, with MM in BCBC and NN in ABAB. Prove that if
∠BNM∠MNC=∠BMN∠NMA\frac{\angle BNM}{\angle MNC}=\frac{\angle BMN}{\angle NMA}
then ABCABC is isosceles.
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