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 :

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 , 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:

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

The centres of two circles C_1 and C_2, each of unit radius are at a distance of 6 units from each other. Let P be the mid point of the line segment joining the centres of C_1 and C_2, and C be a circle touching circles C_1 and C_2 externally. If a common tangent to C_1 and C passing through P is also a common tangent to C_2 and C. then the radius of the circle 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), C_(2) be two circles touching each other externally at the point A and let AB be the diameter of circle C_(1) . Draw a secant BA_(3) to circle C_(2) , intersecting circle C_(1) at a point A_(1)(neA), and circle C_(2) at points A_(2) and A_(3) . If BA_(1) = 2 , BA_(2) = 3 and BA_(3) = 4 , then the radii of circles C_(1) and C_(2) are respectively

The centres of two circles C1 and C2 each of unit radius are at a distance of 6 units from each other. Let P be the mid point of the line segment joining the centres of C1 and C2 and C be a circle touching circles C1 and C2 externally. If a common tangent to C1 and C passing through P is also a common tangent to C2 and C, then the radius of the circle C is

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).

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: