本文首先介绍三角形线段比中的两个有用定理 .定理 1　在△ ABC中 ,E为 BC上一点 ,任作一直线分别交 AB、AE、AC于 P、N、Q,若记 BEEC=λ,则PNNQ=λ.APAB.ACAQ.证明　如图 1所示 ,在△ ABE和△ AEC中 ,由正弦定理可得sinα=BE .sin∠ 1AB ,sinβ =EC .sin∠ 2AC . 图 1∵　∠ 1 In this paper, we first introduce two useful theorems in the ratio of triangle line segments. Theorem 1 In △ ABC, E is a point on BC. Let A, AE, and AC be in P, N, and Q, respectively. If note BEEC=λ, Then PNNQ = λ.APAB.ACAQ. As shown in Figure 1, in △ ABE and △ AEC, from the sine theorem can be obtained sinα = BE .sin ∠ 1AB, sinβ = EC. Sin ∠ 2AC. Figure 1 ∵ ∠ 1