The angle subtended by the chord x+y-1=0 of the circle x^2+y^2=1 at the origin is

Step-by-step solution

To find the angle subtended by the chord x+y=1 at the center of the circle x^2+y^2=1 , we can follow these steps: Identify the Circle and Chord: The given circle is x^2+y^2=1 , which has its center at the origin (0,0) and a radius of 1 . The chord is given by the line equation x+y=1 . Find the Points of Intersection: To find the points where the chord intersects the circle, we can substitute y=1-x into the circle's equation: x^2+(1-x)^2=1 Expanding this: aligned & x^2+ (1-2 x+x^2 )=1 & 2 x^2-2 x+1=1 & 2 x^2-2 x=0 &