Question 59
Two circles $C$ and $C'$ intersect at two points $P$ and $Q$. The line joining the centers meets $C$ at $R$ and $C'$ at $R'$, the line joining $P$ and $R'$ meets $C$ at $X \neq P$ and the line joining $P$ and $R$ meets $C'$ at $X' \neq P$. If the three points $X$, $Q$, $X'$ are collinear, you are asked to:
1. find the angle $\angle XPX'$.
2. prove that $(d+r-r')(d-r+r') = rr'$, where $d$ is the distance between the centers of the circles and $r$ and $r'$ are their radii.
1. find the angle $\angle XPX'$.
2. prove that $(d+r-r')(d-r+r') = rr'$, where $d$ is the distance between the centers of the circles and $r$ and $r'$ are their radii.