If `theta` is the angle between the two radii (one to each circle) drawn from one of the point of intersection of two circles `x^2+y^2=a^2` and `(x-c)^2+y^2=b^2,` then prove that the length of the common chord of the two circles is `(2a bsintheta)/(sqrt(a^2+b^2-2a bcostheta))`

Consider the circle x^(2)+y^(2)=9 and x^(2)+y^(2)-10x+9=0 then find the length of the common chord of circle is

If the circles x^2+y^2-2x-2y+7=0 and x^2+y^2+4x+2y+k=0 cut orthogonally, then the length of the common chord of the circles is a.(12)/(sqrt(13)) b. 2 c. 5 d. 8

If the circles x^(2)+y^(2)+2gx+2fy+c=0 bisects x^(2)+y^(2)+2g'x+2f'y+c'=0 then the length of the common chord of these two circles is -

The length of the common chord of the circles (x-a)^(2)+y^(2)=r^(2) and x^(2)+(y-b)^(2)=r^(2) is

Consider two circles C_(1):x^(2)+y^(2)=25 and C_(2):(x-alpha)^(2)+y^(2)=16 , where alpha in(5,9) . Let the angle between the two radii (one to each circle) drawn from one of the intersection points of C_(1) and C_(2) be sin^(-1)((sqrt(63))/(8)) .If the length of common chord of C_(1) and C_(2) is beta ,then the value of (alpha beta)^(2) equals________.

If the circle x^(2)+y^(2)-2x-2y-1=0 bisects the circumference of the circle x^(2)+y^(2)=1 then the length of the common chord of the circles is

The angle between the tangents drawn from a point on the director circle x^(2)+y^(2)=50 to the circle x^(2)+y^(2)=25 , is