Two circles with equal radii are intersecting at the points (0, 1) and (0, –1). The tangent at the point (0, 1) to one of the circles passes through the centre of the other circle. Then the distance between the centres of these circles is :

If the area of an equilateral triangle inscribed in the circle x² + y² + 10x + 12y + c = 0 is $$27\sqrt 3 $$ sq units then c is equal to :

If a circle C passing through the point (4, 0) touches the circle x² + y² + 4x – 6y = 12 externally at the point (1, – 1), then the radius of C is :

If the circles

x² + y² $$-$$ 16x $$-$$ 20y + 164 = r²  

and  (x $$-$$ 4)² + (y $$-$$ 7)² = 36

intersect at two distinct points, then :