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圆是初中平面几何重要的基础知识之一,也是数学竞赛的热点。本文将国内各级各类初中数学竞赛试题中有关圆的试题选择一部分归纳整理介绍给读者,这些试题大多出于专家和名家之手,构思巧妙,题目新颖别致,富于思考性和趣味性,初中数学爱好者可以从中受到启发和锻练,提高自己的应试能力。 一、线段的计算与证明 例1 已知⊙O直径AB,过A作切线AC,且使AC=AB,连结OC交⊙O于D,连结BD并延长交AC于E,求证:AE=CD,(1983年,芜湖市) 证明:连结AD,∵AC是⊙O的切线,
The circle is one of the important basic knowledge of plane geometry in junior high school and it is also a hot spot in the math competition. This article summarizes and presents to the reader some of the questions related to the circle in the examination questions of various types of junior high school mathematics competitions at home and abroad. These questions are mostly from the hands of experts and masters, they are well-designed, they are novel and unique, they are full of thinking and interesting. Junior mathematics enthusiasts can be inspired and trained to improve their test-taking skills. 1. Calculation and Proof of Line Segments Example 1 It is known that ⊙O diameter AB and A exceed tangent AC, and AC=AB, connect OC to O to D, link BD and extend AC to E, verify: AE=CD , (1983, Wuhu City) Proof: link AD, ∵AC is the tangent of ⊙O,