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**niharika_kumar****Member**- From: Numeraland
- Registered: 2013-02-12
- Posts: 965

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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,311

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

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

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,311

hi bobbym,

Angle bisectors.

Bob

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,664

Hi Bob;

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.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,311

hi bobbym,

Bob

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,664

Hi bob;

I agree with your angle bisector idea. At present, I do not know how that formula was derived.

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.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,311

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 bundy (2013-10-27 00:18:13)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,664

Hi bob;

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

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.

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(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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,311

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

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,311

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

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'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,664

Hi;

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.

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The person above can explain post 3

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,664

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.

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.

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So, there is a deleted post?

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,664

You can say it is an overwritten post.

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.

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Did you know that 'Niharika' means Nebula?

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,664

I did not know that. But how would I?

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.

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**niharika_kumar****Member**- From: Numeraland
- Registered: 2013-02-12
- Posts: 965

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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bobbym wrote:

But how would I?

You could have asked me.

@Niharika, I know. I am bengali too.

'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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,311

hi niharika_kumar

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

Bob

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**niharika_kumar****Member**- From: Numeraland
- Registered: 2013-02-12
- Posts: 965

@agnishom, well but i am not a bengali!

friendship is tan 90°.

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