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命题设△ABC中,AB=c,BC=a,AC=b,∠B,∠C的平分线为BT_1=t_b,CT_2=t_c.若t_b=t_c,求证b=c.这个熟知的命题以往通常是用反证法证明的(如见梁绍鸿著,《初等数学复习及研究》,人民教育出版社,北京,1958年,P95—96)。最近,武汉教育学院郑隆炘老师精心构造了两个全等三角形,并且运用四点共圆等知识,直接证明了它(见《中学生数学》1983年4期,P24)。我们在学习由三角形三边长求有关线段长时,求
The proposition is set in △ABC, AB=c, BC=a, AC=b, ∠B, 平C bisector is BT_1=t_b, CT_2=t_c. If t_b=t_c, verify b=c. This well-known proposition used to be It is usually proved by counter-evidence (for example, see Liang Shaohong, Elementary Mathematics Review and Research, People’s Education Press, Beijing, 1958, P95-96). Recently, Zheng Longxuan of the Wuhan Institute of Education carefully constructed two congruent triangles and used the knowledge of four-point co-circulation to directly prove it (see “Middle School Mathematics”, Issue 4, 1983, p24). When we learn about the length of the triangle from the three sides of the triangle,