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在讲授高中《平面解析几何)(甲种本)173页例2:“求圆心是C(a,o),半径是口的圆的极坐标方程”的基础上,我引导学生推导了“点弦距公式”,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、点弦距公式已知A、B为圆ρ=2acosθ上的二点,它们的极角分别为θ_1和θ_2(θ_1<θ_2),从极点O作OH⊥AB,垂足为H,求证:OH=2a·cosθ_1cosθ_2。证如图1,∵∠OBH=∠OCA,
In teaching High School “Plane Analytic Geometry” (A type of book), page 173. Example 2: “Come the center of the circle is C (a, o), the radius is the polar coordinate equation of the circle of the mouth”, and I guide the student to derive “points” Chord Distance Formula" and illustrated its application. Practice has proved that this will be of great benefit in broadening the horizons of students and improving the ability to comprehensively solve problems. First, point chord distance formula A and B are known to be two points on the circle ρ=2acosθ, their polar angles are θ_1 and θ_2 (θ_1<θ_2), respectively, from the pole O for OH⊥AB, the foot is H, verification : OH=2a·cosθ_1cosθ_2. As shown in Figure 1, ∵∠OBH=∠OCA,