Here we see inversion first. O is point O , but the center of the big circle O' is not point O' . Point O' is inverted point of point O .
Colored parts correspond each other.
Push down the small circle O , without changing the size, to point P . Then QPR is spread out, and the big circle O' gets bigger and bigger. And circle O' leaves point P for far up. At this moment, line QPR is not broken but straight. The big circle O' has always touched lines PQ and PR so that it must now be on the line QPR .