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

Text
 Published Version
Download (150kB)  Preview 
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 

Uncontrolled Keywords:  Triangle, Acute, Obtuse, Perpendicular, Angle bisector, Incentre, Excentre, Collinear 
Subjects:  Natural Sciences > Mathematics 
Divisions:  Azim Premji University > University publications > At Right Angles 
Depositing User:  Mr. Sachin Tirlapur 
Date Deposited:  15 Sep 2018 11:08 
Last Modified:  17 Sep 2018 06:49 
URI:  http://publications.azimpremjifoundation.org/id/eprint/1351 
Publisher URL:  http://apfstatic.s3.apsouth1.amazonaws.com/s3fs... 
Actions (login required)
View Item 
Altmetric
CORE (COnnecting REpositories)