920 Some geometry problems from recent journals
Crux 2813, proposed by Barry Monson, University of New Brunswick,
Fredericton, NB and J. Chris Fisher, University of Regina, Regina,
SK, Canada
Suppose thatMis the midpoint of sideABof the squareABCD. Let
PandQbe the points of intersections of the lineMDwith the circle,
centerM, radiusMA(=MB), wherePis inside the square andQis
outside. Prove that the rectangleAP BQis a golden rectangle, that is,
PB:PA=(