利用轨迹求解三角形中的最值问题

• 作 者: 王尊甫
• 机 构: 山东省平度第一中学,
• 出 处: 中学生理科应试
• 发表日期: 2017年08期
• 关键词: 最值问题 数量关系 三求 外接圆半径 正弦定理 知当 三条 公共点 数量积 基本不等式

三角形中有三个内角和三条边.解三角形主要是应用三角形中的已知边角信息求解其它边或角,常规是“知三求三”的模式.也就是说,在三角形中,只要知道了其中的三个边或角的信息(三条边、两边及一角、两角及一边)均可求出其余的边或角.如果条件中仅给出两项信息,那么对应的三角形就可能会有无数个,在这个形状及数量关系不定的三角形中,就会产生最值.本文将试图用轨迹的角度切入,求解特定条件下三角形中的最值.

Triangle has three interior angles and three sides. Triangulation mainly uses the known corner information in the triangle to solve other edges or corners, and convention is the pattern of “three things in three.” In other words, in the triangle, If you know the information of the three sides or corners (three sides, two sides and one corner, two corners and one side), you can find the remaining sides or corners. If the condition gives only two pieces of information, then the corresponding triangle There will be countless numbers that will produce the most value in a triangle whose shape and number are indeterminate.This paper attempts to find the best value in a triangle under certain conditions by trying to cut in with the angle of the trajectory.