Integer-sided Triangles with perpendicular medians

Maneesha, Ampagouni Divya (2016) Integer-sided Triangles with perpendicular medians. At Right Angles, 5 (1). pp. 27-30. ISSN 2582-1873

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Abstract

I t is well known (and easy to prove) that given any triangle ABC, there exists a triangle whose three sides are respectively congruent to the three medians of △ABC. This triangle is sometimes called the median triangle of △ABC. (Note that this is not the same as the medial triangle, which is the triangle whose vertices are the midpoints of the sides of the triangle. The two notions must not be confused with each other.) In this note, we ask for the condition that must be satisfied by the sides of △ABC in order that its median triangle be right-angled. After obtaining the condition, we consider the problem of generating integer triples (a, b, c) that satisfy this condition.

Item Type: Articles in APF Magazines
Authors: Maneesha, Ampagouni Divya
Document Language:
Language
English
Uncontrolled Keywords: Pythagoras theorem, Apollonius theorem, triangle, median, Diophantine equation
Subjects: Natural Sciences > Mathematics
Divisions: Azim Premji University > University Publications > At Right Angles
Full Text Status: Public
URI: http://publications.azimpremjifoundation.org/id/eprint/3109
Publisher URL:

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