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Question

If two chords having lengths a2-1 and 3a+1, where a is a constant of a circle bisect each other, then the radius of the circle is


A

6

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B

152

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C

8

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D

192

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E

10

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Solution

The correct option is B

152


Explanation for the correct answer:

Finding the radius of the circle:

Two chords of a circle bisect each other only when both are the diameter of a circle.

As both the chords are diameter,

a2-1=3a+1a2-3a-4=0a2-4a+a-4=0aa-4+1a-4=0a-4a+1=0a=4or-1

But radius cannot be negative

So, a=4 and the radius of the circle is,

=3a+12radius=d2=152

Hence, the correct option is B.


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