More variations on the Steiner-Lehmus theme

摘要

The celebrated Steiner-Lehmus theorem states that if the internal bisectors of two angles of a triangle are equal, then the triangle is isosceles. In other words, if P is the incentre of triangle ABC, and if BP and CP meet the sides AC and AB at B′ and C′, respectively, then BB′ = CC′ ? AB = AC; (1) see Figure 1(a). Of course, the converse of (1) follows trivially from symmetry.