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#1 2014-03-04 16:17:58
Cyclic Quadrilateral
Imagine there is a cyclic quadrilateral of sides x,y, z and d. If d is the diameter of the circle in which the quadrilateral is inscribed, then find d in terms of x, y and z.
Any hints?
'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'
I'm not crazy, my mother had me tested.
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#2 2014-03-04 16:29:15
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Cyclic Quadrilateral
Hi;
You might begin with RIPOSTP. A countryman of yours called Parameshvara knew this much:
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#3 2014-03-04 17:20:39
Re: Cyclic Quadrilateral
What is the R in the equation?
'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'
I'm not crazy, my mother had me tested.
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#4 2014-03-04 20:37:05
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Cyclic Quadrilateral
The R is the diameter of the circle. Same as your d.
Manipulate d to 1 side.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#5 2014-03-04 20:51:00
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,643
Re: Cyclic Quadrilateral
hi Agnishom,
You mention d twice so I'm hoping the diagram below is what you want.
I cannot see a way to finish this off but this may be a way to do this.
Similarly,
where
So if you can find a way to eliminate the angles from this, what you'd be left with is the required formula.
Note: Following my comment on another post, I've figured out how to put Greek letters onto my diagrams. 
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 2014-03-04 22:50:24
Re: Cyclic Quadrilateral
I'll try to do something.
By the way, what package are you using?
'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'
I'm not crazy, my mother had me tested.
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#7 2014-03-04 23:53:02
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,643
Re: Cyclic Quadrilateral
I use Geometer's Sketchpad. It is much the same as geogebra but it's not free. I got it before geogebra existed and I've stuck with it as I'm used to how it works. The colour options are quite good, so it's nice for making diagrams where I want to colour code bits to make it easier to understand. I used it recently for http://www.mathisfunforum.com/viewtopic.php?id=20495 and all my fractions diagrams are made that way too.
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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#8 2014-03-05 00:28:12
Re: Cyclic Quadrilateral
Not free in the sense 'freedom denying'?
'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'
I'm not crazy, my mother had me tested.
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#9 2014-03-05 01:06:47
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,643
Re: Cyclic Quadrilateral
That's correct. I keep it trapped inside this black case and only let it out when I choose.
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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#10 2014-03-05 01:11:52
Re: Cyclic Quadrilateral
black case? your laptop?
'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'
I'm not crazy, my mother had me tested.
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#11 2014-03-05 01:41:25
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,643
Re: Cyclic Quadrilateral
Here's a picture of my black top. And, for comparison, my multi-coloured top. I did try to get a 'lap' picture too; but these proved to be unsuitable for this forum.
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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#12 2014-03-05 01:51:27
Re: Cyclic Quadrilateral
Wow, the second picture looks something like the thing at the end of this:
I guess its platonic and is called octahedron.
By the way, a concurrent discussion about 'top' was going on: http://mathisfunforum.com/viewtopic.php … 50#p303550 (Post 8160)
'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'
I'm not crazy, my mother had me tested.
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#13 2014-03-07 15:08:39
Re: Cyclic Quadrilateral
ProblemA cyclic quadrilateral ABCD has the following lengths, AB=80, BC=91, and CD=280 Find AD if AD is also the diameter of the circumscribed circle.
'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'
I'm not crazy, my mother had me tested.
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#14 2014-03-07 20:56:58
- phrontister
- Real Member
- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,895
Re: Cyclic Quadrilateral
Hi Agnishom,
Here's what I got with some T&E on Geogebra (rounded to 1 decimal place). All I have to do now is find some formulas for that. 
"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson
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#15 2014-03-07 21:24:10
- phrontister
- Real Member
- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,895
Re: Cyclic Quadrilateral
Update: Geogebra reveals that AC = 165 and ∠ ACD is a right angle...
"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson
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#16 2014-03-07 21:48:40
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Cyclic Quadrilateral
Hi;
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#17 2014-03-07 23:00:14
Re: Cyclic Quadrilateral
@phrontister,
Great Work! Thank You
@bobbym,
Thank You
Where did you get this from? What is it called?
I do not see what the first code does. Please explain that one.
The geogebra way is easier? I do not even have an idea how to begin
'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'
I'm not crazy, my mother had me tested.
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#18 2014-03-07 23:06:25
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Cyclic Quadrilateral
The first code does the substitution.
The formula was given in post #2.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
Offline
#19 2014-03-07 23:08:55
Re: Cyclic Quadrilateral
There is an error in post 4. That confused me
'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'
I'm not crazy, my mother had me tested.
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#20 2014-03-07 23:10:58
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Cyclic Quadrilateral
Yes, I meant radius but for some reason said diameter. It appears I like to double things whenever possible.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
Offline
#21 2014-03-07 23:16:53
Re: Cyclic Quadrilateral
The only thing I am left with is to compute the result.
'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'
I'm not crazy, my mother had me tested.
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#22 2014-03-07 23:21:43
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Cyclic Quadrilateral
Please add this to the solutions over there if you like. But make sure you do the manipulations by hand, then they will be happy.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
Offline
#23 2014-03-07 23:47:03
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,643
Re: Cyclic Quadrilateral
hi
ACD is a right angle...
Because it's the angle subtended by a diameter. So this leads to a simpler formula:
So by cosine rule on ABC
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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#24 2014-03-08 00:34:11
Re: Cyclic Quadrilateral
Please add this to the solutions over there if you like. But make sure you do the manipulations by hand, then they will be happy.
I'll only quote the formula. They are brilliant, they'll figure out the rest.
'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'
I'm not crazy, my mother had me tested.
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#25 2014-03-08 00:37:21
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Cyclic Quadrilateral
Hmmm, that reasoning has a big hole in it.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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