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Circles C1 and C2 are externally tangent...

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)`.

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