有些平面几何证明题，若能根据题设条件，恰当地构造一元二次方程，然后用一元二次方程及其性质来证，往往能少作或不作辅助线，使证题途径简捷明快，从而提高学生灵活运用知识的能力．一、判别式的绝妙作用根据题设条件，构造出一元二次方程，然后巧妙地运用到别式，使问题迎 Some plane geometry proofs, if they can be constructed according to the conditions, properly construct a quadratic equation, and then use the one-quadratic quadratic equation and its properties to prove that it is often possible to make little or no auxiliary lines, so that the testimony approach is simple and straightforward. Improve students’ ability to use knowledge flexibly. First, the wonderful role of discriminant based on the conditions set out to construct a one-dimensional quadratic equation, and then cleverly applied to other types, so that the problem