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#1 2013-10-27 16:52:26

niharika_kumar
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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.

#2 2013-10-27 20:16:38

bob bundy
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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


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

#3 2013-10-27 22:41:21

bob bundy
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Re: triangles and circles

hi bobbym,

Angle bisectors.  smile smile smile

Bob


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

#4 2013-10-27 22:59:46

bobbym
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Re: triangles and circles

Hi Bob;


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#5 2013-10-27 23:10:20

bob bundy
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Re: triangles and circles

hi bobbym,



Bob


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

#6 2013-10-27 23:16:19

bobbym
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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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#7 2013-10-27 23:16:37

bob bundy
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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


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Last edited by bob bundy (2013-10-27 23:18:13)


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

#8 2013-10-27 23:28:07

bobbym
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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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#9 2013-10-27 23:47:09

Agnishom
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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'
'Who are you to judge everything?' -Alokananda

#10 2013-10-28 00:04:40

bob bundy
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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

#11 2013-10-28 02:41:27

bob bundy
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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

#12 2013-10-28 02:51:53

Agnishom
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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'
'Who are you to judge everything?' -Alokananda

#13 2013-10-28 03:13:48

bobbym
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Re: triangles and circles

Hi;


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#14 2013-10-28 03:19:48

Agnishom
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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'
'Who are you to judge everything?' -Alokananda

#15 2013-10-28 03:23:32

bobbym
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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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#16 2013-10-28 03:43:35

Agnishom
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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'
'Who are you to judge everything?' -Alokananda

#17 2013-10-28 04:58:09

bobbym
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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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#18 2013-10-28 23:48:23

Agnishom
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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'
'Who are you to judge everything?' -Alokananda

#19 2013-10-29 01:03:33

bobbym
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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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#20 2013-10-29 23:07:52

niharika_kumar
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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.

#21 2013-10-29 23:32:41

Agnishom
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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'
'Who are you to judge everything?' -Alokananda

#22 2013-10-29 23:54:54

bob bundy
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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

#23 2013-10-30 03:27:18

niharika_kumar
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Re: triangles and circles

@agnishom, well but i am not a bengali!


friendship is tan 90.

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