Borislav Borisov,
Deyan Dimitrov,
Nikolay Ninov,
Teodor Hristov
Mathematics High School – Lovech
Abstract. The article is a scientific work of student under the supervision of Associate Professor Dr. Veselin Nenkov. The new results in it were awarded first prize at the International Competition “Methodology and Information Technology in Education” in 2019. The article refers to loci determined by notable points in a triangle, generated by equilateral triangles with vertices on a constant circle. The construction of the triangle is similar to the initial one from the First International “Network research project” with the participation of Bulgaria, Kazakhstan, and Russia. The main difference between those two constructions consists in the location of two pairs of vertices of the two equilateral triangles – in the initial problem they are on a constant line, but in the present one – on a circle. The loci are circles, ellipses, and curves of fourth order.
Keywords: equilateral triangle; circle; ellipse; curve of fourth degree
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