论文部分内容阅读
轨迹,作为平面几何的一部分,其解题思想、方法与其它内容多有不同。轨迹问题的解决常离不开几何证明,这是广为人知的。但是,轨迹用于几何证明,却并不多见。本文中的轨迹法就是有关这方面的探讨。应用轨迹法解题时,首先要明确与几何证明有关的轨迹,然后再从适当的轨迹中选出特殊元素,给出待证问题的证明。下面我们结合例子作些说明。例1 过△ABC的边BC、CA、AB上的点A_1、B_1、C_1引其垂线。这些垂线相交于一点的充要条件是: A_1B~2+B_1C~2+c_1A~2=A_1C~2+C_1B~2+B_1A~2 分析:由边AB的垂线,自然联想到“满足XA~2-XB~2=k的点X的轨迹是已知线段
The trajectory, as a part of plane geometry, has many different ideas and methods for solving problems. The solution to the trajectory problem is often inseparable from the geometric proof, which is widely known. However, trajectories are used for geometrical proof, but they are rare. The trajectory method in this article is a discussion about this aspect. When using the trajectory method to solve a problem, the trajectory related to the geometrical proof must be clearly defined first, and then special elements should be selected from the appropriate trajectories to prove the problem to be proved. Below we use some examples to illustrate. Example 1 The points A_1, B_1, and C_1 on the sides BC, CA, and AB of the ΔABC lead to their vertical lines. The necessary and sufficient conditions for the intersection of these perpendicular lines at one point are: A_1B~2+B_1C~2+c_1A~2=A_1C~2+C_1B~2+B_1A~2 Analysis: Naturally associated with the vertical line of the side AB, “Satisfaction XA The point X trace of ~2-XB~2=k is a known line segment