(1) Given radius of bigger circle is 9cm.

Length of segment MT = 9cm.

(2) MT = MN+NT [M-N-T]

9 = MN+2.5 [Given radius of smaller circle is 2.5]

MN = 9-2.5

MN = 6.5cm.

(3) RM touches smaller circle at S.

MR is the tangent to the smaller circle. NS is the radius of smaller circle.

NSM = 90˚ [Tangent theorem]

In NSM , NS^{2}+MS^{2 }= MN^{2}

2.5^{2}+MS^{2} = 6.5^{2}

MS^{2} = 6.5^{2}-2.5^{2}

MS^{2} = 42.25-6.25

MS^{2} = 36

MS = 6

MR = SR+SM [R-S-M]

9 = SR+6

SR = 9-6 = 3

MS:SR = 6:3 = 2:1