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2012年全国初中数学竞赛题中,几个较难的几何题的解法均蕴含于教材中,注意到这些信息则赛题迎刃而解.例析如下.一、结论直用例1(2012年全国初中数学竞赛题)如图1,⊙O的内接四边形AB-CD中,AC、BD是它的对角线,AC中点I是△ABD的内心.求证:(1)OI是△IBD的外接圆的切线;(2)AB+AD=2BD.分析结论(1)是三角形内心性质的直接运用.I为△ABD的内心,则易知∠CID=∠CDI,从而CD=CI=CB,故C为△BDI外接圆圆心.又I为弦AC中点,因此OI⊥AC.
2012 national junior high school mathematics competition questions, several difficult geometric problems are contained in the textbook solution, noting that the information is the subject solved .Examples are as follows.ConclusionIndeed 1 (National Junior Middle School Mathematics Competition in 2012 Title) As shown in Figure 1, ⊙ O inscribed quadrilateral AB-CD, AC, BD is its diagonal, AC midpoint I is the heart of △ ABD. Proof: (1) OI is △ IBD circumcircle Tangent line; (2) AB + AD = 2BD. Analysis Conclusion (1) is the direct use of the inner properties of the triangle .I is the inner center of △ ABD, then easy to know ∠CID = ∠CDI, so CD = CI = CB, so C △ BDI circumcircle center and I for the string AC midpoint, so OI⊥AC.