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解析几何的基本方法是坐标法,但解析几何问题的“魂”还是“几何”特征,只要抓住几何特征,也可以从平面几何角度来巧妙解决解析几何难题,本文举例说明.一、利用圆的重要性质涉及直线与圆的位置关系的题,一般是联立直线与圆的方程求解,但由于圆具有特殊的几何性质,如对称性、圆周角定理、垂径定理、弦切角定理、相交弦定理、切割线定理和圆幂定理等,所以,只要抓住了其几何特征,问题往往迎刃而解.
The basic method of analytic geometry is the coordinate method. However, the “soul” or the “geometric” feature of the geometric problem can be analytically solved. As long as the geometric features are grasped, the geometrical problem can be cleverly solved from the geometrical perspective. First, the use of the important properties of the circle involves the relationship between the position of the straight line and the problem is generally straight line and the circle equation to solve, but because of the circle has a special geometric properties, such as symmetry, circular angle theorem, Cut angle theorem, intersection string theorem, cutting line theorem and round power theorem, so long as to seize the geometric features, the problem is often solved.