Fagnano's problem Addendum

Shirali, Shailesh (2017) Fagnano's problem Addendum. At Right Angles, 6 (1). pp. 25-28.

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Abstract

The problem treated in the accompanying article is this: Given an arbitrary acute-angled triangle PQR, inscribe within it a triangle ABC, with A on side RP, B on side PQ, and C on side QR, having the smallest possible perimeter. The author establishes, using geometrical arguments, that in the optimal configuration, the following triangle similarities must hold (see Figure 1): △ARC ∼ △QBC ∼ △ABP ∼ △QRP, and then shows, using trigonometry, that these conditions force A, B, C to be the feet of the altitudes of the triangle.

Item Type:	Articles in APF Magazines
Authors:	Shirali, Shailesh
Document Language:	Language English
Uncontrolled Keywords:	Triangle, Acute, Obtuse, Perpendicular, Angle bisector, Incentre, Excentre, Collinear
Subjects:	Natural Sciences > Mathematics
Divisions:	Azim Premji University - Bengaluru > University Publications > At Right Angles
Full Text Status:	Public
URI:	http://publications.azimpremjiuniversity.edu.in/id/eprint/1351
Publisher URL:	http://apfstatic.s3.ap-south-1.amazonaws.com/s3fs-...

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