Fagnano's problem Addendum
Shirali, Shailesh (2017) Fagnano's problem Addendum. At Right Angles, 6 (1). pp. 2528.

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Abstract
The problem treated in the accompanying article is this: Given an arbitrary acuteangled 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: 


Uncontrolled Keywords:  Triangle, Acute, Obtuse, Perpendicular, Angle bisector, Incentre, Excentre, Collinear  
Subjects:  Natural Sciences > Mathematics  
Divisions:  Azim Premji University > University Publications > At Right Angles  
Full Text Status:  Public  
URI:  http://publications.azimpremjiuniversity.edu.in/id/eprint/1351  
Publisher URL:  http://apfstatic.s3.apsouth1.amazonaws.com/s3fs... 
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