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A circle with centre at (2, 4) is such t...

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

A

`sqrt(41)` cm

B

`sqrt(11)` cm

C

`sqrt(21)`cm

D

`sqrt(31)`cm

Text Solution

Verified by Experts

The correct Answer is:
A
Let `r` be the radius of the circle.

Now perpendicular distance
`AC=(|2+4+2|)/(sqrt(1^(2)+1^(2)))`
`=8/(sqrt(2))=4sqrt(2)`
In right angled `DeltaCAB`,
`r^(2)=(AC)^(2)+(AB)^(2)`
`=(4sqrt(2))^(2)+(3)^(2)=32+9`
`impliesr^(2)=41`
`:.r=sqrt(41)`
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