最值问题广泛分布于数学的各个知识点中,而对与圆有关的最值问题不少同学感到困惑,事实上,在处理与圆相关的最值问题时,应注意正确地画出相应的图形,寻求特殊位置,分析运动过程中的变量与不变量,建立必要的关系,及时将问题转化,进而获取答案,现举例说明.一、求最大值例1(2016·泸州)如图1,在平面直角坐标系中,已知点A(1,0),B(1-a,0),C(1+a,O)(a>0),点P在以D(4,4)为圆心,1为半径的圆上运动,且始终满足∠BPC=90°,则a的 Most value problems are widely distributed in the various knowledge points in mathematics, and most of the circle-related problems most students are confused, in fact, in dealing with the circle of the most valuable issues, should pay attention to correctly draw the corresponding Graphics, to find a special position, analysis of the movement process variables and invariants, the establishment of the necessary relations, the timely transformation of the problem, and then get the answer, an example of a maximum value of Example 1 (2016 · Luzhou) In the Cartesian coordinate system, points A (1,0), B (1-a, 0) and C (1 + a, 0) As the center of the circle, a radius of the circular motion, and always meet ∠ BPC = 90 °, then the