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1.试题2016年北京市中学生数学竞赛高中一年级初赛填空第8题是这样一道题目:例1如图1,D为△ABC内一点,并且满足AB=CD=4,∠A+∠BDC=1800,试确定S△ABC-S△BDC的最大值.试题考查了四点共圆、等腰梯形、平行四边形的判定与性质以及两边已知的三角形面积最值问题.试题综合性强,解法灵活,考查了数形结合、转化等数学思想及割补的解题方法,检测了推理及分析问题与解决问题的能力.如何添加辅助线是本题的难点,要充分利用已知条件从构造圆、全等三角形入手解决.
1. Test questions 2016 Beijing high school students math contest high school first round of fill in the sky 8 is such a problem: Example 1 As shown in Figure 1, D is △ ABC within a point, and meet AB = CD = 4, ∠ A + ∠ BDC = 1800 , Try to determine the maximum value of S △ ABC-S △ BDC.This test examines the four point total circle, isosceles trapezoid, the parallelogram of the judgment and the nature and the triangle on both sides of the known value of the most value problems. Comprehensive test questions, flexible solution , Examines the mathematical combination of shape, transformation and other mathematical ideas and the problem-solving method to detect the reasoning and analysis of the problem and the ability to solve the problem.How to add aids is the difficulty of this problem, we should make full use of known conditions from the construction of the circle, Triangle triangulation to solve.