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

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.

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:

A circle C touches the x-axis and the circle x ^(2) + (y-1) ^(2) =1 externally, then locus of the centre of the circle C is given by

A circle C_(1) of radius 2 units rolls o the outerside of the circle C_(2) : x^(2) + y^(2) + 4x = 0 touching it externally. The locus of the centre of C_(1) is

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

Let C_(1) and C_(2) be externally tangent circles with radius 2 and 3 respectively.Let C_(1) and C_(2) both touch circle C_(3) internally at point A and B respectively.The tangents to C_(3) at A and B meet at T and TA=4, then radius of circle C_(3) 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 :

A relation R is defined on the set of circles such that " C_(1)RC_(2)implies circle C_(1) and circle C_(2) touch each other externally", then relation R is