Ramachandran, A.
(2015)
Triangle centres in an isosceles triangle.
At Right Angles, 4 (3).
pp. 3034.
Abstract
Every triangle has certain lines associated with it. The most prominent among them are the perpendicular bisectors of the sides, the bisectors of the angles, the altitudes, and the medians. Figure 1 represents a scalene triangle ABC, with AB<AC. Also shown are the altitude AD from A to BC, the bisector AE of angle A, the median AF where F is the midpoint of BC, and the perpendicular bisector of BC.
We must justify the order in which these lines appear in the figure: the altitude is the closest to AB (the shorter of the sides AB and AC), then the angle bisector, followed by the median, and the perpendicular bisector is closest to side AC. It is of interest to see whether this ordering can be justified using the regular results of Euclidean geometry.
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