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#1 2013-10-26 17:52:26

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 1,021

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 bundy
Moderator
Registered: 2010-06-20
Posts: 6,380

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

View Image: kumar2.gif

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

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#3 2013-10-26 23:41:21

bob bundy
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Registered: 2010-06-20
Posts: 6,380

Re: triangles and circles

hi bobbym,

Angle bisectors.  smile smile smile

Bob

View Image: kumar5.gif

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

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#4 2013-10-26 23:59:46

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,366

Re: triangles and circles

Hi Bob;


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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#5 2013-10-27 00:10:20

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,380

Re: triangles and circles

hi bobbym,

Bob


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

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#6 2013-10-27 00:16:19

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,366

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#7 2013-10-27 00:16:37

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,380

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.  sad

Bob

View Image: kumar4.gif

Last edited by bob bundy (2013-10-27 00:18:13)


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

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#8 2013-10-27 00:28:07

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,366

Re: triangles and circles

Hi bob;

Check this page out. This point of intersection is called the incenter.

http://en.wikipedia.org/wiki/Incenter


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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#9 2013-10-27 00:47:09

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,665
Website

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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#10 2013-10-27 01:04:40

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,380

Re: triangles and circles

Agnishom wrote:

(iv) radius = y.

Why?

Bob Bundy wrote:

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


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

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#11 2013-10-27 03:41:27

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,380

Re: triangles and circles

hi bobbym,

You wrote:

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


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

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#12 2013-10-27 03:51:53

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,665
Website

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'
'Humanity is still kept intact. It remains within.' -Alokananda

Online

#13 2013-10-27 04:13:48

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,366

Re: triangles and circles

Hi;


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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#14 2013-10-27 04:19:48

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,665
Website

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'
'Humanity is still kept intact. It remains within.' -Alokananda

Online

#15 2013-10-27 04:23:32

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,366

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#16 2013-10-27 04:43:35

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,665
Website

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'
'Humanity is still kept intact. It remains within.' -Alokananda

Online

#17 2013-10-27 05:58:09

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,366

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#18 2013-10-28 00:48:23

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,665
Website

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'
'Humanity is still kept intact. It remains within.' -Alokananda

Online

#19 2013-10-28 02:03:33

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,366

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#20 2013-10-29 00:07:52

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 1,021

Re: triangles and circles

wow ,such a long thread following my ques. cool
@bob i found the ans. as radius= 2cm. thnx for your help.
@agnishom yes its meaning is nebula smile
@bobbym thnx


friendship is tan 90°.

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#21 2013-10-29 00:32:41

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,665
Website

Re: triangles and circles

bobbym wrote:

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'
'Humanity is still kept intact. It remains within.' -Alokananda

Online

#22 2013-10-29 00:54:54

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,380

Re: triangles and circles

hi niharika_kumar

Yes, your question certainly sparked some interest.  And 2 cm is the answer everyone got.  smile

Bob


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

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#23 2013-10-29 04:27:18

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 1,021

Re: triangles and circles

@agnishom, well but i am not a bengali!


friendship is tan 90°.

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