[" 26.Circles "C_(1)" and "C_(2)" are externally tangertand they the tremalytangert "],[" of "C_(1)" and "C_(2)" are "4" and "10" ,respectively and the civentres of the tree circles an "],[" is also common internaltangent of "C_(1)" and "C_(2)" .Given that the length of the "],[n" and "p" are positive integers,"m" and "p" are relatively prime and "n" is not div "],[" corien find the value of "(m+n+p)" ."]

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).

if C_(2)=n then find the value of (m+1)C_(4)

If p and q are the greatest values of ""^(2n)C_(r) and ""^(2n-1)C_(r) respectively, then

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 , 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:

If ""^(n)P_r = ""^(n)P_(r-1) and ""^(n)C_(r) = ""^(n)C_(r-1) , find the values of n and r.

If ""^(2n)C_(1), ""^(2n)C_(2) and ""^(2n)C_(3) are in A.P., find n.

If n is a positive integer and C_4 = ""^nC_r then find the value of sum_(x = 1)^n r^2 ((C_r)/(C_(r - 1)) )