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 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

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 of radii R and r ,R > r touch each other externally then the radius of circle which touches both of them externally and also their direct common tangent, is R (b) (R r)/(R+r) (R r)/((sqrt(R)+sqrt(r))^2) (d) (R r)/((sqrt(R)-sqrt(r))^2)

Two circles with radii 25 cm and 9 cm touch each other externally. Find the length of the direct common tangent.

Three circles with radius r_(1), r_(2), r_(3) touch one another externally. The tangents at their point of contact meet at a point whose distance from a point of contact is 2 . The value of ((r_(1)r_(2)r_(3))/(r_(1)+r_(2)+r_(3))) is equal to

Circles with radii 3, 4 and 5 touch each other externally. If P is the point of intersection of tangents to these circles at their points of contact, then if the distance of P from the points of contact is lambda then lambda_2 is _____

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

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 with radii a and b touch each other externally such that theta is the angle between the direct common tangents, (a > bgeq2) . Then prove that theta=2sin^(-1)((a-b)/(a+b)) .