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**niharika_kumar****Member**- From: Numeraland
- Registered: 2013-02-12
- Posts: 1,028

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: 6,469

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
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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: 88,998

Hi Bob;

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,469

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: 88,998

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 agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,469

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: 88,998

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.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bob bundy****Moderator**- Registered: 2010-06-20
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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: 6,469

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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,998

Hi;

**In mathematics, you don't understand things. You just get used to them.**

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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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,998

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.**

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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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,998

You can say it is an overwritten post.

**In mathematics, you don't understand things. You just get used to them.**

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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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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I did not know that. But how would I?

**In mathematics, you don't understand things. You just get used to them.**

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**niharika_kumar****Member**- From: Numeraland
- Registered: 2013-02-12
- Posts: 1,028

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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,469

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: 1,028

@agnishom, well but i am not a bengali!

friendship is tan 90°.

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