圆(x-1)^2+(y-1)^2=4被直线x-y+2=0截得的弦对应的劣弧所对的圆心角为

Question

圆(x-1)^2+(y-1)^2=4被直线x-y+2=0截得的弦对应的劣弧所对的圆心角为

Answer 1

设圆(x-1)^2+(y-1)^2=4与直线x-y+2=0交点为A、B
圆心C(1,1)到直线x-y+2=0的距离
d=|1-1+2|/√2=√2
半径R=2
R=2=√2d
所以∠ABC=∠BAC=45°,
截得的弦对应的劣弧所对的圆心角∠BCA=90°