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Question

A circle with Centre at (2,4)is such that the line x+y+2=0cuts a chord of length 6.

The radius of the circle is


A

41

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B

11

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C

21

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D

31

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Solution

The correct option is A

41


The explanation for the correct option:

Step1. Draw the diagram :

The length of the perpendicular from (2,4) on the line x+y+2=0 is

AC=|2(1)+4(1)+2|12+12=82=42

Step2. To find the radius of the circle:

Let r be the radius of the circle.

The perpendicular from the center onto a chord bisects it.

So, the base of the triangle so formed would be 3.

AB=3

In a right-angled triangle CAB,

r2=(AC)2+(AB)2r2=(42)2+(3)2r2=32+9r=41

Hence the correct option is (A).


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