A circle `C_(1)` passes through the centre of the circle `C_(2);x^(2)+y^(2)=4` and gets bisected at its point of intersection with `C_(2)` .The radius of `c_(1)` is equal to:

Statement-1: The centre of the circle passing through the points (0, 0), (1, 0) and touching the circle C : x^(2)+y^(2)=9 lies inside the circle. Statement-2: If a circle C_(1) passes through the centre of the circle C_(2) and also touches the circle, the radius of the circle C_(2) is twice the radius of circle C_(1)

If a circle passes through the point (a,b) and cuts the circle x^(2)+y^(2)=4 orthogonally,then the locus of its centre is

If a circle passes through the point (a,b) and cuts the circle x^(2)+y^(2)=4 orthogonally, then the locus of its centre is

If a circle passes through the point (1, 1) and cuts the circle x^(2)+y^(2)=1 orthogonally, then the locus of its centre is

If a circle C passing through the point (4,0) touches the circle x^(2)+y^(2)+4x-6y=12 externally at the point (1,-1) ,then the radius of C is

A circle C_(1) of radius 2 units rolls o the outerside of the circle C_(2) : x^(2) + y^(2) + 4x = 0 touching it externally. The locus of the centre of C_(1) is

If a circle Passes through a point (1,2) and cut the circle x^(2)+y^(2)=4 orthogonally,Then the locus of its centre is