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. Number of common tangents to the circles `x^2 + y^2 - 6x = 0 and x^2 + y^2 + 2x = 0` is (A) 1 (B) 2 (C) 3 (D) 4

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. circles x^2 + y^2 + 2ax + c^2 = 0 and x^2 + y^2 + 2by + c^2 = 0 touche each other if (A) 1/a^2 + 1/b^2 = 2/c^2 (B) 1/a^2 + 1/b^2 = 2/c^2 (C) 1/a^2 - 1/b^2 = 2/c^2 (D) 1/a^2 - 1/b^2 = 4/c^2

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 circles having radii r_1 and r_2 intersect orthogonally. Find the length of their common chord.

Two soap bubbles A and B have radii r_(1) and r_(2) respectively. If r_(1) lt r_(2) than the excess pressure inside

Two fixed circles with radii r_1 and r_2,(r_1> r_2) , respectively, touch each other externally. Then identify the locus of the point of intersection of their direction common tangents.

Two circles of radii r_(1) and r_(2), r_(1) gt r_(2) ge2 touch each other externally. If theta be the angle between the direct common tangents, then,

Two circle with radii r_(1) and r_(2) respectively touch each other externally. Let r_(3) be the radius of a circle that touches these two circle as well as a common tangents to two circles then which of the following relation is true

The radical axis of two circles having centres at C_(1) and C_(2) and radii r_(1) and r_(2) is neither intersecting nor touching any of the circles, if

The insulated spheres of radii R_(1) and R_(2) having charges Q_(1) and Q_(2) respectively are connected to each other. There is

The insulated spheres of radii R_(1) and R_(2) having charges Q_(1) and Q_(2) respectively are connected to each other. There is