在讲授部编六年制重点高中数学“平面解析几何》173页例2:“求圆心是C(α,0),半径是α的圆的极坐标方程”的基础上,我引导学生推导了“点切距公式”,并举例说明了它的应用。实践证明,这对于开阔学生视野,提高综合解题能力是大有益处的。一、点切距公式已知A为圆ρ=2αcosθ上一点,它的极角为θ_A,从极点O作OH垂直于过A点的切线,垂足为H,求证:OH=2αcos~2θ_A In the lecturer’s department, he compiled six-year key high school mathematics “Plane Analytical Geometry” (page 173). Example 2: “The center of the circle is the polar coordinate equation of C(α, 0) and the radius is α.” Based on this, I guide students to derivation. The “point cut distance formula” has been used as an example to illustrate its application. Practice has proved that this is a great benefit to broaden students’ horizons and improve the comprehensive problem-solving abilities.1. Point cut distance formula A is known as circle ρ=2αcosθ. At one point, its polar angle is θ_A. From the pole O, the OH is perpendicular to the tangent line passing through point A. The foot is H. Prove that: OH=2αcos~2θ_A