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**Richard Chen****Guest**

Hi everyone! I am new to this website and I need a bit of help with this problem. I do not need you to answer the problem for me, just walk me through a few steps/hints and I will try to solve it on my own.

In triangle ABC, AB = AC, and angle A is equal to 36 degrees. Point D is on line AC so that line 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 = \frac{y}{x}. Write the equation from Part (b) in terms of r, and find r.

(d) Find cos(36) and cos(72) using Parts a-c.

This is a problem from the Introduction to Geometry course at Art of Problem Solving.

**RCKittenLover****Member**- From: KittenLand
- Registered: 2020-06-17
- Posts: 3

I should add that I have completed the first three parts, and I am just stuck on part (d). Thank you in advance!

Cats restore sanity

Rule of math: If it seems easy, you're doing it wrong.

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 8,908

hi RCKittenLover

Welcome to the forum.

THis has appeared before here:

http://www.mathisfunforum.com/viewtopic.php?id=22416

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

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**RCKittenLover****Member**- From: KittenLand
- Registered: 2020-06-17
- Posts: 3

Hello! It seems that the link you have given me is from quite a while ago. Should I continue it?

Cats restore sanity

Rule of math: If it seems easy, you're doing it wrong.

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 8,908

It's the same problem. Looks like your teachers are re-cycling old worksheets.

The posts go on a bit. As you've got to part d, skip to post 11.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

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**RCKittenLover****Member**- From: KittenLand
- Registered: 2020-06-17
- Posts: 3

Okay, thank you!

Cats restore sanity

Rule of math: If it seems easy, you're doing it wrong.

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