Thread: euclidean construction of the regular pentagon

using trigonometry in right triangle ABF in unit circle O with diameter AB of length 2, show that AF=t and cos(theta) = t/2, so that theta = 36, measure of angleFOB=72, and the construction yields a regular pentagon.

I can not for the life of me figure this out. The construction steps are 1. starting with diameter AB, construct CO perpendicular to AB. 2. Construct the midpoint D of AO. 3. construct point E on AB so that DE = DC. 4. Construct point F on the circle so that AF= AE. 5. Draw segment BF. This is a side of the regular pentagon.
I am confused.

Originally Posted by janae77

using trigonometry in right triangle ABF in unit circle O with diameter AB of length 2, show that AF=t and cos(theta) = t/2, so that theta = 36, measure of angleFOB=72, and the construction yields a regular pentagon.

I can not for the life of me figure this out. The construction steps are 1. starting with diameter AB, construct CO perpendicular to AB. 2. Construct the midpoint D of AO. 3. construct point E on AB so that DE = DC. 4. Construct point F on the circle so that AF= AE. 5. Draw segment BF. This is a side of the regular pentagon.
I am confused.

Have a look here: Pentagon - Wikipedia, the free encyclopedia

Scroll down a little bit until you came to the item "Construction"