CAT 2020 Exam Shift 2 Solved Paper

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Question : 73 of 76

Marks: +1, -0

Let

{C} 1

and

{C} 2

be concentric circles such that the diameter of

{C} 1

is

2 {cm}

longer than that of

C 2 .

If a chord of

{C} 1

has length

6 {cm}

and is a tangent to

{C} 2

, then the diameter, in

{cm}

, of

{C} 1

is

Your Answer:

Solution:

Given,

d+2=D ⇒ r+1=R

In the figure

O T=r

and

O B=r+1

O T ⟂ A B

as

{AB}

is the tangent
OT bisects AB i.e.,

T B=\;{6}/{2}=3

Now, in

∆ O T B, O T^{2}+T B^{2}=O B^{2}

∴ r^{2}+3^{2}=(r+1)^{2} ⇒ r=4

∴ D=2(R)=2(r+1)=10 {cm}

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