In figure 3.86, circle with centre M touches the circle with centre N at point T.

Radius RM touches the smaller circle at S. Radii of circles are 9 cm and 2.5 cm. Find the answers to the following questions hence find the ratio MS:SR.

(1) Find the length of segment MT
(2) Find the length of seg MN
(3) Find the measure of NSM.


(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 , NS2+MS= MN2
2.52+MS2 = 6.52
MS2 = 6.52-2.52
MS2 = 42.25-6.25
MS2 = 36
MS = 6
MR = SR+SM [R-S-M]
9 = SR+6
SR = 9-6 = 3
MS:SR = 6:3 = 2:1

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