一道试题的探究

• 作 者: 陈辉
• 机 构: 江苏省兴化市周庄高级中学,
• 出 处: 中学生数学
• 发表日期: 2014年23期
• 关键词: 托勒密定理 等腰直角三角形 凸四边形 当且仅当 不小于 正弦定理 数据运算 理得 逆时针旋转

一、试题展示2014年泰州市高三第三次调研测试的第14题是:在△ABC中,BC=2(1/2),AC=1,以AB为边作等腰直角三角形ABD(B为直角顶点,C、D两点在直线AB的两侧).当∠C变化时,线段CD长的最大值为.二、背景探究本题的背景是托勒密定理:凸四边形两组对边乘积之和不小于两条对角线的乘积,等号当且仅当四边形为圆内接四边形时取得.

First, the test questions Taizhou City, the third high school in 2014 the third test test question 14 is: In △ ABC, BC = 2 (1/2), AC = 1, with AB as the side of the isosceles right triangle ABD For the right-angle vertex, C, D two points on both sides of the line AB). When ∠C changes, the maximum length of the line segment CD is 2. Background to explore The background of this question is the Ptolemy Theorem: The sum of the products is not less than the product of two diagonal lines, the equals sign if and only if the quadrilateral is a quadrilateral of circles.