Long medians and long angle bisectors

Following Euler, we denote the side lengths and angles of a triangle ABC by a, b, c, A, B, C in the standard order. Any line segment joining a vertex of ABC to any point on the opposite side line will be called a cevian , and a cevian AA′ of length t will be called long, strictly long, or balanced according as t ≥ a, t > a or t = a . If A′ lies strictly between B and C , AA′ is called an internal cevian . This convention regarding cevians is not universal, and it is, for example, in a heavy contrast with that in [1, p. 73].