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北京市朝阳区2015高三二模数学(文)试题及答案(扫描版)

北京市朝阳区2015高三二模数学(文)试题及答案(扫描版)
北京市朝阳区2015高三二模数学(文)试题及答案(扫描版)

2015北京海淀东城西城等城区中考二模数学分类--第26题几何阅读题

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3.(东城)26 .阅读材料 如图1,若点P 是⊙O 外的一点,线段PO 交⊙O 于点A,则PA 长是点P 与⊙O 上各点之间的最短距离. 图1 图2 证明:延长PO 交⊙O 于点B ,显然PB>PA . 如图2,在⊙O 上任取一点C (与点A ,B 不重合),连结PC ,OC . ,,,, PO PC OC PO PA OA OA OC PA PC <+=+=∴<且 ∴PA 长是点P 与⊙O 上各点之间的最短距离. 由此可以得到真命题:圆外一点与圆上各点之间的最短距离是这点到圆心的距离与半径的差. 请用上述真命题解决下列问题. (1)如图3,在Rt △ABC 中,∠ACB =90°,AC =BC =2,以BC 为直径的半圆交AB 于D ,P 是上的一 个动点,连接AP ,则AP 长的最小值是 . 图3 (2)如图4,在边长为2的菱形ABCD 中,∠A =60°,M 是AD 边的中点,点N 是AB 边上一动点,将△AMN 沿MN 所在的直线翻折得到△MN A ' ,连接C A ' ,①求线段A ’M 的长度; ②求线段C A ' 长的最小值. 图4

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2020年北京市东城区中考数学二模试卷(解析版)

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