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A = 36^o, AB = AC, C-bisector intersects AB at D, find BC without trig

Source: Spanish Mathematical Olympiad 1994 P4

July 31, 2018
geometryisoscelestrigonometry

Problem Statement

In a triangle ABCABC with ∠A=36o \angle A = 36^o and AB=ACAB = AC, the bisector of the angle at CC meets the oposite side at DD. Compute the angles of △BCD\triangle BCD. Express the length of side BCBC in terms of the length bb of side ACAC without using trigonometric functions.
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