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

View Item 