Question

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. $\sqrt{31}cm$

Answer 1

Answer: (A)

Let $r$ be the radius of the circle.

Now, perpendicular distance
$AC=\frac{|2+4+2|}{\sqrt{1^2+1^2}}=\frac{8}{\sqrt{2}}$
$=4\sqrt{2}$
In right angled $\Delta CAB$,
$r^2=(AC{)}^2+(AB{)}^2$
$=(4\sqrt{2}{)}^2+(3{)}^2=32+9$
$\Rightarrow r^2=41$
$\Rightarrow r=\sqrt{41}$