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1988年第一届“祖冲之杯”初中数学邀请赛有这样一道题: 例1 如图,在直角三角形ABC中,∠A=90°,AB=6~(1/2),中线AN与中线BM垂直,则BM=____. 问题的求解本身没有多大的困难,但细细分析两条中线互相垂直的三角形,却获得了如下优美的性质. 性质1 若三角形有两条中线互相垂直,则第三条中线与这条中线所对应的边之比为
In 1988, the first “Zuchong Chongzhi Cup” junior high school mathematics invitational tournament had such a question: Example 1 As shown in the figure, in the right-angled triangle ABC, ∠A=90°, AB=6~(1/2), and the midline AN is perpendicular to the midline BM. , BM=____. The problem itself is not difficult to solve, but a detailed analysis of the two vertical lines perpendicular to the triangle, but obtained the following beautiful nature. Nature 1 If the triangle has two midlines perpendicular to each other, the third The ratio of the midline to the edge of this midline is