`C_1 and C_2` are fixed circles of radii `r_1 and r_2` touches each other externally. Circle 'C' touches both Circles `C_1 and C_2` extemelly. If `r_1/r_2=3/2` then the eccentricity of the locus of centre of circles C is

A circle touches the line L and the circle C_(1) externally such that both the circles are on the same side of the line, then the locus of centre of the circle is :

Let C , C_1 , C_2 be circles of radii 5,3,2 respectively. C_1 and C_2 , touch each other externally and C internally. A circle C_3 touches C_1 and C_2 externally and C internally. If its radius is m/n where m and n are relatively prime positive integers, then 2n-m is:

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,

3 circles of radii a, b, c (a lt b lt c) touch each other externally and have x-axis as a common tangent then

The circles having radii 1, 2, 3 touch cach other externally then the radius of the circle which cuts three circles orthogonally is

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.

Let C_1 and C_2 be two circles with C_2 lying inside C_1 A circle C lying inside C_1 touches C_1 internally and C_2 externally. Identify the locus of the centre of C

ABCD is a square of side length 2 units. C_(1) is the circle touching all the sides of the square ABCD and C_(2) is the circumcircle of square ABCD. L is a fixed line in the same plane and R is fixed point. If a circle is such that it touches the line L and the circle C_(1) externally, such that both the circles are on the same side of the line, then the locus of centre of the circle is

Consider circles C_(1) and C_(2) touching both the axes and passing through (4, 4), then the product of the radii of the two circles is

Let ABCD be a square of side length 2 units. C_(2) is the fircle through the vertices A, B, C, D and C_(1) is the circle touching all the of the square ABCD. L is a lien through vertex A. A circle touches the line L and the circle C_(1) externally such that both the circles are on the same side of the line L. The locus of the centre of the circle is