直线√3X+Y-2√3=0截圆x^2+y^2=4所得的劣弧所对的圆心角为 A:π/6 B:π/4 C:π/3 D:π/2

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直线√3X+Y-2√3=0截圆x^2+y^2=4所得的劣弧所对的圆心角为A:π/6B:π/4C:π/3D:π/2直线√3X+Y-2√3=0截圆x^2+y^2=4所得的劣弧所对的圆心角为A:π/6B:π

直线√3X+Y-2√3=0截圆x^2+y^2=4所得的劣弧所对的圆心角为 A:π/6 B:π/4 C:π/3 D:π/2
直线√3X+Y-2√3=0截圆x^2+y^2=4所得的劣弧所对的圆心角为 A:π/6 B:π/4 C:π/3 D:π/2

直线√3X+Y-2√3=0截圆x^2+y^2=4所得的劣弧所对的圆心角为 A:π/6 B:π/4 C:π/3 D:π/2
将直线y=2√3-√3x 代入圆的方程并化简得到
4x^2-12x-8=0
x^2-3x+2=0
设直线与圆的两交点坐标分别为(x1,y1)(x2,y2)
则x1+x2=3 x1x2=2
(x1-x2)^2=(x1+x2)^2-4x1x2=9-8=1
(y1-y2)^2=[(2√3-√3x1)-(2√3-√3x2 )]^2
=(√3x2-√3x1)^2=3
所以弦长=√[(y1-y2)^2+(x1-x2)^2]=2
弦长等于半径,所以烈弧所对圆心角为60度