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**niharika_kumar****Member**- From: Numeraland
- Registered: 2013-02-12
- Posts: 1,062

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: 7,651

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

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,651

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,262

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.****No great discovery was ever made without a bold guess. **

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,651

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,262

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.****No great discovery was ever made without a bold guess. **

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,651

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)*

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: 105,262

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.****No great discovery was ever made without a bold guess. **

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(iv) radius = y.

Why?

'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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,651

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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,651

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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'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,262

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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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'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,262

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.****No great discovery was ever made without a bold guess. **

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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'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,262

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.****No great discovery was ever made without a bold guess. **

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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'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,262

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.****No great discovery was ever made without a bold guess. **

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**niharika_kumar****Member**- From: Numeraland
- Registered: 2013-02-12
- Posts: 1,062

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'

I'm not crazy, my mother had me tested.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,651

hi niharika_kumar

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

Bob

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

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**niharika_kumar****Member**- From: Numeraland
- Registered: 2013-02-12
- Posts: 1,062

@agnishom, well but i am not a bengali!

friendship is tan 90°.

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