If the circles `x^2+y^2-16x-20y+164=r^2` and `(x-4)^2+(y-7)^2=36` intersect at two points then (a) `1ltrlt11` (b) `r=11` (c) `rgt11` (d) `0ltrlt1`

The two circles x^2+ y^2=r^2 and x^2+y^2-10x +16=0 intersect at two distinct points. Then

If the two circles (x+1)^2+(y-3)^2=r^2 and x^2+y^2-8x+2y+8=0 intersect at two distinct point,then (A) r > 2 (B) 2 < r < 8 (C) r < 2 (D) r=2

If two circles (x-1)^(2)+(y-3)^(2)=r^(2) and x^(2)+y^(2)-8x+2y+8=0 intersect in two distinct points , then

If the two circles (x-2)^(2)+(y+3)^(2) =lambda^(2) and x^(2)+y^(2) -4x +4y-1=0 intersect in two distinct points then :

Two circles centres A and B radii r_1 and r_2 respectively. (i) touch each other internally iff |r_1 - r_2| = AB . (ii) Intersect each other at two points iff |r_1 - r_2| ltAB lt r_1+ r_2 . (iii) touch each other externally iff r_1 + r_2 = AB . (iv) are separated if AB gt r_1 + r_2 . Number of common tangents to the two circles in case (i), (ii), (iii) and (iv) are 1, 2, 3 and 4 respectively. If circles (x-1)^2 + (y-3)^2 = r^2 and x^2 + y^2 - 8x + 2y + 8=0 intersect each other at two different points, then : (A) 1ltrlt5 (B) 5ltrlt8 (C) 2ltrlt8 (D) none of these

The angle between the circles x^2+y^2-2x-4y+3=0 and x^2+y^2-4x-6y+11=0 is

If one end of a diameter of the circle x^2 + y^2 - 8x - 14y+c=0 is the point (-3, 2) , then its other end is the point. (A) (5, 7) (B) (9, 11) (C) (10, 11) (D) (11, 12)

The tangent to the circle x^(2)+y^(2)-4x+2y+k=0 at (1,1) is x-2y+1=0 then k=

Let A be the centre of the circle x^(2)+y^(2)-2x-4y-20=0 . If the tangents at the points B (1, 7) and D(4, -2) on the circle meet at the point C, then the perimeter of the quadrilateral ABCD is

Point on the circle x^(2)+y^(2)-2x+4y-4=0 which is nearest to the line y=2x+11 is :