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!)

 Oct 8, 2020

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