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题目:(2013年陕西中考数学第23题)如图1,直线l与⊙O相切于点D,过圆心O作EF∥l交⊙O于E、F两点,点A是⊙O上一点,连接AE、AF,并分别延长交直线l于B、C两点.(1)求证:∠ABC+∠ACB=90°;(2)当⊙O的半径R=5,BD=12时,求tan∠ACB的值.自2003年以来,陕西中考数学第23题皆以圆为背景放置三角形或四边形来检测学生的推理能力和运算水平,由于考查内容丰富多变,对学生分析问题、解决问题
Topic: (Shaanxi Senior High School Mathematics Question 23 in 2013) As shown in Fig. 1, the straight line l is tangent to the ⊙O at point D. The over center O is used as the EF∥l and the crossover O is located at E and F. The point A is ⊙O. One point, connect AE, AF, and extend the intersection line l respectively to B, C two points. (1) verification: ∠ ABC + ∠ ACB = 90 °; (2) When ⊙ O radius R = 5, BD = 12, Finding the value of tan ∠ ACB. Since 2003, the Shaanxi Provincial Entrance Examination Mathematics Question 23 has placed triangles or quadrilaterals on the background of a circle to test students’ reasoning ability and level of calculation. Because of the rich and varied contents of the examination, the students are analyzed and solved. problem