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2013年北京大学保送生招生考试笔试于2012年12月22日举行,其中数学试题与往年一样,仍为五道,但难度下降.下面笔者对今年北大保送生数学试题作一简要分析评解.1.已知△ABC内一点M满足∠CMB=100°,线段MB的垂直平分线交边AB于点P,线段CM的垂直平分线交边AC于点Q,若P,M,Q三点共线,求∠CAB的大小.分析本题考查三角形的内角与外角的关系及线段垂直平分线性质的基本应用.解由∠CMB=100°得∠MBC+∠BCM一80°;又因为P,M,Q三点共线,
2013 Peking University Paul give students admission exam written test held on December 22, 2012, of which math test as in previous years, is still five, but the difficulty decreased.After I give a brief analysis of this year’s Peking University students to send a mathematical analysis. 1. It is known that a point M in △ ABC satisfies ∠CMB = 100 °. The vertical bisector of line segment MB intersects with point AB at point P. The vertical bisector of line segment CM intersects at point Q. If P, M, Q are three points Collinear, find the size of CAB.Analysis of the problem to examine the relationship between the internal angle and the external angle of the triangle and the basic application of the nature of the vertical bisector of the line segment.The solution by ∠CMB = 100 ° ∠MBC + ∠BCM a 80 °; and because P, M , Q three-point total line,