(Solved): The figure below shows a fixed circle \( C_{1} \) with equation \( (x-1)^{2}+y^{2}=1 \) and anothe ...

The figure below shows a fixed circle \( C_{1} \) with equation \( (x-1)^{2}+y^{2}=1 \) and another shrinking circle \( C_{2} \) centered at the origin with positive \( y \)-intercept \( P=(0, r) \). Let \( Q \) be the point of intersection between the two circles pictured, draw a line through \( P \) and \( Q \) and let \( R \) be the \( x \)-intercept of that line. (a) Find the coordinates of the point \( Q \); your answers will involve \( r \) : \( Q=( \) (b) The line through \( P \) and \( Q \) has equation \[ \mathrm{y}=\frac{r}{2}\left(1-\sqrt{\frac{\left(1-r^{2}\right)}{4}}\right) \times\left(-\frac{2}{r}\right)\left(1-\sqrt{1-\left(\frac{r^{2}}{4}\right)}\right) \mathrm{x}+ \] (c) The point \( R=( \)