If the length of the chord of the circle x^2+y^2=r^2 (r0) along the line y-2x=3 is r, the…

Question

If the length of the chord of the circle $x^2+y^2=r^2$ ($r>0$) along the line $y-2x=3$ is $r$, then $r^2$ is equal to:

Accepted Answer

Distance from origin to $2x-y+3=0$: $d=\dfrac3{\sqrt5}$.

Chord length $=2\sqrt{r^2-d^2}=r\Rightarrow r^2-d^2=\dfrac{r^2}4\Rightarrow\dfrac34r^2=d^2=\dfrac95\Rightarrow r^2=\dfrac{12}5.$

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