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## #1 2020-06-17 06:39:14

Richard Chen
Guest

### Geometry Problem

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.

## #2 2020-06-17 09:16:29

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

### Re: Geometry Problem

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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## #3 2020-06-17 09:27:40

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

### Re: Geometry Problem

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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## #4 2020-06-17 09:44:29

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

### Re: Geometry Problem

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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## #5 2020-06-17 09:46:49

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

### Re: Geometry Problem

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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## #6 2020-06-17 09:49:32

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

### Re: Geometry Problem

Okay, thank you!

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

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