C’ is on AC and B’ is
C’B’ // CB
As AB’ = B’C’
Triangle AB’C is an isosceles triangle.
By similarity triangle ABC is
BK is the height of triangle ABC and bisects AC.
of the pentagon equals b(1+√5)/2 or
Triangles BMO and BNO are
Then MN // AC
Triangles B’MO, ONR (and UBS) are
congruent and isosceles.
Then B’M = OM = ON = NR = OS = bΦ
of angles triangle PTO is isosceles, then PQ
= OQ and OMPN is
a rhombus, so PM = NP = ON = OM
Subsequently, triangle AMP is isosceles
and PM = AM = B’M = bΦ
shown in the picture below, points A, B' and O are concyclic (circle
with center M);
so are points M, U, S, and N (circle with center O).
Since AB’ =
a = 2bΦ
Then a/b = 2Φ=