In triangle ABC, AB = AC, and angle A is equal to 36 degrees. Point D is on AC so that BD bisects angle ABC.
(a) Prove that BC = BD = AD.
(b) Let x = BC and let y = CD. Using similar triangles BCD and ABC, write an equation involving x and y.
(c) Let r = y/x. Write the equation from part (b) in terms of r, and find r.
(d) Find cos 36 degrees and cos 72 degrees using Parts a-c. (Do not use your calculator!)