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众所周知,三角形的角平分线性质定理:三角形内(外)角的平分线内(外)分对边的比等于两邻边的相应比。若把角平分线换成一般线段,则有如下更一般的结论: 定理1 三角形的顶点与对边任一内点连得的线段内分对边的比,等于该线段与两邻边所成夹角的正弦乘以相应邻边之积的比。 定理2 三角形的顶点与对边延长线上任一点连得的线段外分对边的比,等于该线段与两邻边所成夹角的正弦乘以相应邻边之积的比。
It is well-known that the nature of the bisector of the triangle is that the ratio of the inner (outer) bisector to the inner bisector of the inner (outer) angle of the triangle is equal to the corresponding ratio between the two neighbors. If the diagonal bisector is replaced by the general line segment, then the following general conclusion is reached: Theorem 1 The ratio between the vertices of the triangle and any inner point of the opposite edge in the line segment equals to the ratio between the line segment and the two adjacent edges The sine of the included angle is multiplied by the product of the products of the corresponding neighbors. Theorem 2 The ratio of the vertex of a triangle to the outer edge of a segment connected at any point on the extension of the opposite side is equal to the ratio of the product of the sine of the included angle of the segment with the two adjacent edges multiplied by the product of the corresponding adjacent edges.