330 Constructions with the golden section
Exercise
1.LetABCbe an equilateral triangle. The line joining the midpoints
D,Eof two sides intersects the circumcircle atF. ThenEdivides
DFin the golden section,i.e.,
DE
DF
=
√
5 − 1
2
.
D
B C
A
F
E
2.M is the midpoint of the sideABof a squareABCD. The line
DMintersects the circle with diameterABat two points,Pinside
andQ outside the square. Show that the rectangleAP BQis a
golden rectangle,i.e.,PB:PA=(
√
5+1):2.
A B
D C
M
P
Q