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))`

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 (2ab sin theta)/(sqrt(a^(2)+b^(2)-2ab cos theta))

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

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

The length of the common chord of the two circles (x-a)^2+(y-b)^2=c^2,(x-b)^2+(y-a)^2=c^2 is

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

If the circle x^(2) +y^(2) + 2gx + 2fy + c = 0 bisects the circumference of the circle x^(2) +y^(2) + 2g'x + 2f'y + c' = 0 , them the length of the common chord of these two circles 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________.

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