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

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Aicharya · Accepted Answer

Let $r$ be the radius of the circle.

Now, perpendicular distance $ \begin{aligned} A C & =\frac{|2+4+2|}{\sqrt{1^2+1^2}}=\frac{8}{\sqrt{2}} \\ & =4 \sqrt{2} \end{aligned} $ In right angled $\triangle C A B$, $ \begin{aligned} r^2 & =(A C)^2+(A B)^2 \\ & =(4 \sqrt{2})^2+(3)^2=32+9 \\ \Rightarrow \quad r^2 & =41 \Rightarrow r=\sqrt{41} \end{aligned} $

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…

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