直线4x-3y-5=0截圆x^2+y^2=4所得的劣弧所对圆心角为A.π/3 B.2π/3 C.5π/6 D.π/2

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直线4x-3y-5=0截圆x^2+y^2=4所得的劣弧所对圆心角为A.π/3B.2π/3C.5π/6D.π/2直线4x-3y-5=0截圆x^2+y^2=4所得的劣弧所对圆心角为A.π/3B.2π/3C

直线4x-3y-5=0截圆x^2+y^2=4所得的劣弧所对圆心角为A.π/3 B.2π/3 C.5π/6 D.π/2
直线4x-3y-5=0截圆x^2+y^2=4所得的劣弧所对圆心角为
A.π/3 B.2π/3 C.5π/6 D.π/2

直线4x-3y-5=0截圆x^2+y^2=4所得的劣弧所对圆心角为A.π/3 B.2π/3 C.5π/6 D.π/2
由4x-3y=5,x^2+y^2=4得25x^2-40x-11=0,设直线与圆的交点分别为(x1,y1),(x2,y2),则x1+x2=8/5,x1*x2=-(11/25).由弦长公式得弧长L=根号下(1+k^2)|x1-x2|=根号下〔1+(4/3)^2〕*根号下〔(x1+x2)^2-4x1x2〕=(5/3)*(6倍根号3/5)=2倍根号3.设所求角为a,由余弦定理得cosa=(4+4-12)/8=-1/2.所以a=120度.