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.

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Articles in APF Magazines

Authors:

Shirali, Shailesh

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