Theorem concerning a right triangle

COMMUNITY MATHEMATICS CENTRE, CoMaC (2017) Theorem concerning a right triangle. At Right Angles, 6 (2). pp. 95-97.

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Abstract

T M α C he following elegant geometric result concerning a triangle is based on a problem that appeared in the Regional Mathematics Olympiad (RMO) of 2016. Let ABC be a scalene triangle, and let D be the midpoint of BC. Draw median AD. Through D draw a line perpendicular to AD and let it meet the extended sides AB, AC at points K, L, respectively. Then points B , C , K , L lie on a circle if and only if angle geometry syllabus at BAC the is a right angle. (See Figure 1.) er and compass is part of the standard is a standard procedure for doing the job, and it is so A simple t to think of an alternative to it that is just as simple, if not procedure, announced in a Twitter post [1]. A B D L C F D K Angle bisector Figure 1 The implication in one direction is easy (if the triangle is right-angled, then the four points are concyclic); but the reverse implication seems more challenging. We shall give a geometric solution for the forward implication, followed by an algebraic solution in which both the implications are established at the same time.

Item Type: Articles in APF Magazines
Uncontrolled Keywords: Cosine rule, intersecting chords theorem, crossed chords G theorem, Apollonius, power of a point
Subjects: Natural Sciences
Natural Sciences > Mathematics
Divisions: Azim Premji University > University publications > At Right Angles
Depositing User: Mr. Sachin Tirlapur
Date Deposited: 15 Sep 2018 14:26
Last Modified: 15 Sep 2018 14:26
URI: http://publications.azimpremjifoundation.org/id/eprint/1374
Publisher URL: http://apfstatic.s3.ap-south-1.amazonaws.com/s3fs-...

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