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 (msqrt(n))/(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).

Circles C_(1) and C_(2) are externally tangent and they are both inter

1.	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 (msqrt(n))/(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).
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