I have a circle that the center goes through $ y = 2x$ and $R=2$.

I need to find the circle equation if it's given that $y = x+3$ cuts the circle in a string of length $\sqrt{8}$.

I drew all this information in GeoGebra $5$ and I think it would look somehow like this:

enter image description here

Besides all the information I created in the drawing, I don't know what more can I do.



Let $D\; :\; x-y+3=0.$

the distance from the center $A(a,2a)$ to $D$ is


$=\sqrt{2}\;\;$ by Phytagoras.



which gives $\;A(1,2)$ or $A(5,10)$

and the equations





Check that distance of $(a,2a)$ from $y=x+3$ should be $\sqrt 2$

Now your turn.


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