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computational in isosceles with vertex angle 36, equal angles (Chile 1991 L2 P6)

Source:

May 27, 2019
anglesangle bisectorAngle Chasinggeometry

Problem Statement

Given a triangle with △ABC \triangle ABC , with: ∠C=36o \angle C = 36^o and ∠A=∠B \angle A = \angle B . Consider the points D D on BC BC , E E on AD AD , F F on BE BE , G G on DF DF and H H on EG EG , so that the rays AD,BE,DF,EG,FH AD, BE, DF, EG, FH bisect the angles A,B,D,E,F A, B, D, E, F respectively. It is known that FH=1 FH = 1 . Calculate AC AC.
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