Hi guys I'm working out a problem which needs me to solve these circle equations but it's been a while since I've had to do this stuff. I need to find the y coordinate of the red circle radius r/4 when its x-coord is r/4 and is also meeting the blue circle radius r.
It seems to me that its possible to work this out with only the given information but am I wrong?
I've tried using both cartesian and parametric equations but it comes out incorrectly. e.g.
$$ (x-\frac{r}{4})^2 + (y-b)^2 - \frac{r^2}{16} = x^2 + y^2 - r^2 $$
$$ x -\frac{r}{4} + y -b = x + y - \sqrt{\frac{15}{16}}r $$
$$ -\frac{r}{4} = - \sqrt{\frac{15}{16}}r +b $$
$$ (\sqrt{\frac{15}{16}}-\sqrt{\frac{1}{16}})r = b $$
$$ \frac{\sqrt{15}-1}{4} = b $$ I'm guessing I might not be allowed to remove x and y or I'm simplifying incorrectly.. Thanks, Dan