One Generalization of the Geometric Problem from 19th Junior Balkan Mathematical Olympiad

1) Ivaylo Staribratov, 2) Radka Todorova

1) University of Plovdiv “Paisii Hilendarski” (Bulgaria)
2) Mathematical School “Academic Kiril Popov” – Plovdiv (Bulgaria)

Abstract. We present one possible generalization, inspired by the usage of the Dynamic Geometry Software GeoGebra, of the geometric problem from the 19th Junior Balkan Mathematical Olympiad. We have presented the process of the generalization in front of students about 16 – 17 years of age from the Mathematical School “Academic Kiril Popov” – Plovdiv. We have use the technique of tree diagrams to ease students’ understanding of the solution and to help them in the steps of the generalization.

Keywords: Math Olympiad; Dynamic geometry software; Experiment; Tree diagram

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