Question

In figure below, 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​

Answer 1

Answer:

The figure is not visible....

Answer 2

Answer:

Hi,

According to the question

let r1 is the radius of bigger circle

r1 = 9 cm

so as to the line segment MR ,MR = 9 cm

Now draw a perpendicular from R to T i.e. RT,RT is equal to radius of small circle,RT =

2.5 cm

Now look at the triangle ∆ MRT,here you know the base and perpendicular,have to calculate hypotenuse from Pythagoras theorem

\begin{gathered} {(mt)}^{2} = \sqrt{( {MR)}^{2} + ( {RT)}^{2} } \\ {(MT)}^{2} = \sqrt{( {9)}^{2} + ( {2.5)}^{2} } \\ = \sqrt{81 + 6.25 } \\ = \sqrt{87.25} \\ MT= 9.34 \: m\end{gathered}

(mt)

2

=

(MR)

2

+(RT)

2

(MT)

2

=

(9)

2

+(2.5)

2

=

81+6.25

=

87.25

MT=9.34m

(2)

length of segmennt MN= MT-TN

= 9.34-2.5

=6.84 cm

3)

angle MNS = 90°

but I am not sure about it