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:

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

Two circles with radii a and b respectively touch each other externally . Let c be the radius of a circle that touches these two circles as well as a common tangent to the circles. Then

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_(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

Circles C_1 and C_2 are externally tangent and they are both internally tangent to the circle C_3. The radii of C_1 and C_2 are 4 and 10, respectively and the centres of the three circles are collinear. A chord of C_3 is also a common internal tangent of C_1 and C_2. Given that the length of the chord is (msqrtn)/p where m,n and p are positive integers, m and p are relatively prime and n is not divisible by the square of any prime, find the value of (m + n + p).

There are two circles C_(1) and C_(2) touching each other and the coordinate axes, if C_(1) is smaller than C_(2) and its radius is 2 units, then radius of C_(2) , 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: