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If the radii of each of the outer circles is r then show that radius of the inner circle is

*Last edited by Agnishom (2012-11-21 15:03:47)*

'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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,070

hi Agnishom

See diagram. Let the radius of the little circle be R

AB = BC = r

AC = R + r (why?)

So you should be able to use Pythagoras here.

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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WOW! Thats a great proof

But what if the examiner asks me How do I know that BC = r (apart from intution)?

'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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,070

OK. Another diagram below.

This one shows a circle in the middle (B) and one on the left that crosses it (A) and one on the right that just touches it (C) .

The tangent to B where it crosses A cuts A again.

The tangent to B where it touches C is also a tangent for C.

General rule. When two circles touch they share a common tangent.

A tangent is always at right angles to the radius at the point where the tangent touches.

So back to the previous diagram:

ABC = 90. If you give a letter to a fourth point, you'll complete a square. So BC = r

And AD is perpendicular to the common tangent at D (haven't drawn this line) and DC is too.

So ADC is a straight line.

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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I see

Thanks

However I will like to ask you again if I have any doubts

'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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,070

Certainly. Geometry and I have a long and happy relationship.

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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**n872yt3r****Member**- Registered: 2013-01-21
- Posts: 392

Did you steal my idea?

- n872yt3r

Math Is Fun Rocks!

By the power of the exponent, I square and cube you!

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**n872yt3r****Member**- Registered: 2013-01-21
- Posts: 392

Keep this comment up; I'm linking it to the GeoGebra Forum.

There are:

4 Circles

22 Squares

24 Triangles

66 Rectangles

72 Irregular

- n872yt3r

Math Is Fun Rocks!

By the power of the exponent, I square and cube you!

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Hi n872yt3r.

WHAT ARE YOU TALKING ABOUT?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**n872yt3r****Member**- Registered: 2013-01-21
- Posts: 392

I'm thinking you stole my idea because I did the same thing on a thread of 3 kissing circles with bobbym.

And the 4 circles etc. is for my upload on the GeoGebra Forum and on this site where you can upload GeoGebra programs.

- n872yt3r

Math Is Fun Rocks!

By the power of the exponent, I square and cube you!

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