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#1 2012-05-23 01:32:33

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,242

What is the chord angle?

Hi;

This problem came up:

In the adjoining figure, Find angle BCD

showimage.php?pid=220409&filename=Circle.png

Let's see if geogebra can give us a clue.

1) Create points A(0,0) and B(5,0).

2) Use the angle with a given size tool and click B and then click A. In the input box enter 30°. Point B' will be created.

3) Draw a line between A and B'.

4) Use the angle with a given size tool and click A and then B' and enter 80°

5) Point A' will be created.

6) Hide point B and draw a line from B' to A'.

7) Get the intersection of the new line and the x axis.

8) Point C will be created. Hide line AB' and B'C.

9) Use the circle through 3 point tool on A, B' and C.

10) Create a polygon with A, B' and C as vertices.

11) Create a point anywhere on the bottom half of the circle's circumference. Call it D.

12) Use the polygon tool on A,C and D. Color the polygon a different color from the top one.

13) Use the angle measure tool to measure angle ADC. What do you get for the angle? Move point D around and observe the angle.

Here is what your picture should look like:

View Image: 2012-05-23_065955.gif

In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#2 2012-05-23 02:24:02

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,623
Website

Re: What is the chord angle?

Hi Bobbym;

Will you give me the mathematical reason why this happens?
I mean how do you come to know that: BCD + BAD = 180


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#3 2012-05-23 06:06:03

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,242

Re: What is the chord angle?

Hi Agnishom;

The purpose of this thread is to use the techniques and software of experimental mathematics to find and soft - prove conjectures. Traditional and rigorous methods that you seek are handled in the other thread.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#4 2012-06-22 03:29:10

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,623
Website

Re: What is the chord angle?

But only the traditional methods can really prove
What can be done with softwares is just illustrations of examples.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#5 2012-06-22 03:38:17

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,520

Re: What is the chord angle?

Actually, it was only with the use of a computer that the conjecture about there being 24 4 dimensional spheres tangent to one 4D sphere.

Computers were also used to prove that a valid sudoku grid must have at least 17 clues given at the beginning.

Last edited by anonimnystefy (2012-06-22 03:39:24)


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#6 2012-06-22 03:40:49

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,242

Re: What is the chord angle?

Hi Agnishom;

Yes, for a rigorous proof you would use traditional methods. But for finding things to apply the traditional methods to, you might try the ideas presented here.

I know that you have only been exposed to the methods of traditional or classical mathematics. This training is geared toward the teaching of the calculus or continuous mathematics.

As you progress you will come into contact with the new "Discrete Mathematics." The methods I am playing with will then be more relevant to you.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#7 2012-06-22 04:17:54

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,378

Re: What is the chord angle?


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

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#8 2012-06-22 05:07:41

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,242

Re: What is the chord angle?

Hi Agnishom;

Yes, follow the link that Bob has provided for the rigorous proof.

Let's see if geogebra can give us a clue.

Remember that line in post #1. That is one of the uses of software and computers. All in all, geogebra did well don't you think. Also, it was fun! Try it, it might even make you change your signature...


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

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