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#1 2013-10-26 17:52:26
- niharika_kumar
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- From: Numeraland
- Registered: 2013-02-12
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triangles and circles
Q.ABC is a triangle, right angled at B. A circle is inscribed in it.The lengths of the 2 sides containing the r8 angle are 6 nd 8 cm
Find the radius of the circle.
friendship is tan 90°.
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#2 2013-10-26 21:16:38
- Bob
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- Registered: 2010-06-20
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Re: triangles and circles
hi niharika_kumar
Diagram below. I've labelled the points where the triangle touches the circle D, E and F and the centre O.
I've then done a similar x, y, z trick, like I did for your previous question.
Note. OFB = 90 as AB is a tangent, ODB = 90 as BC is a tangent and ABC = 90 was given.
So OFBD is a square. => once we know 'y', we also know the radius.
Method:
(i) Work out AC using Pythagoras.
(ii) Make equations for x + y, for x + z, and for y + z.
(iii) Find x, y, and z.
(iv) radius = y.
Let me know when you get an answer and I'll check it for you.
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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#3 2013-10-26 23:41:21
- Bob
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Re: triangles and circles
hi bobbym,
Angle bisectors.
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 2013-10-26 23:59:46
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: triangles and circles
Hi Bob;
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 2013-10-27 00:10:20
- Bob
- Administrator
- Registered: 2010-06-20
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Re: triangles and circles
hi bobbym,
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 2013-10-27 00:16:19
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: triangles and circles
Hi bob;
I agree with your angle bisector idea. At present, I do not know how that formula was derived.
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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#7 2013-10-27 00:16:37
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,643
Re: triangles and circles
hi bobbym,
edit: I think I have a book with it in but it's just been put back in the loft. 
Bob
Last edited by Bob (2013-10-27 00:18:13)
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 2013-10-27 00:28:07
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: triangles and circles
Hi bob;
Check this page out. This point of intersection is called the incenter.
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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#9 2013-10-27 00:47:09
Re: triangles and circles
(iv) radius = y.
Why?
'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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#10 2013-10-27 01:04:40
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,643
Re: triangles and circles
(iv) radius = y.
Why?
Note. OFB = 90 as AB is a tangent, ODB = 90 as BC is a tangent and ABC = 90 was given.
So OFBD is a square. => once we know 'y', we also know the radius.
B
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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#11 2013-10-27 03:41:27
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,643
Re: triangles and circles
hi bobbym,
Check this page out.
Arhh yes. I thought it had shades of Heron's formula in it. My book has the proof for Heron, so that sews it up nicely. Thanks.
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 2013-10-27 03:51:53
Re: triangles and circles
'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 2013-10-27 04:13:48
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: triangles and circles
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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#14 2013-10-27 04:19:48
Re: triangles and circles
The person above can explain post 3
'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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#15 2013-10-27 04:23:32
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: triangles and circles
Yes, there was a geogebra post I was working on. When I got to the end of it, it did not work. That is bob's improvement which I used in the new post.
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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#16 2013-10-27 04:43:35
Re: triangles and circles
So, there is a deleted post?
'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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#17 2013-10-27 05:58:09
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: triangles and circles
You can say it is an overwritten post.
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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#18 2013-10-28 00:48:23
Re: triangles and circles
Did you know that 'Niharika' means Nebula?
'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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#19 2013-10-28 02:03:33
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: triangles and circles
I did not know that. But how would I?
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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#20 2013-10-29 00:07:52
- niharika_kumar
- Member
- From: Numeraland
- Registered: 2013-02-12
- Posts: 1,062
Re: triangles and circles
wow ,such a long thread following my ques. 
@bob i found the ans. as radius= 2cm. thnx for your help.
@agnishom yes its meaning is nebula
@bobbym thnx
friendship is tan 90°.
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#21 2013-10-29 00:32:41
Re: triangles and circles
But how would I?
You could have asked me.
@Niharika, I know. I am bengali too.
'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 2013-10-29 00:54:54
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,643
Re: triangles and circles
hi niharika_kumar
Yes, your question certainly sparked some interest. And 2 cm is the answer everyone got.
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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#23 2013-10-29 04:27:18
- niharika_kumar
- Member
- From: Numeraland
- Registered: 2013-02-12
- Posts: 1,062
Re: triangles and circles
@agnishom, well but i am not a bengali!
friendship is tan 90°.
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