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#1 2012-11-21 15:00:35

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,785
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4 kissing circles

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

View Image: Circle.jpg

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

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#2 2012-11-21 21:03:24

bob bundy
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Registered: 2010-06-20
Posts: 6,528

Re: 4 kissing circles

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

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

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#3 2012-11-22 01:17:48

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,785
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Re: 4 kissing circles

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

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#4 2012-11-22 01:28:51

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,528

Re: 4 kissing circles

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

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

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#5 2012-11-22 01:36:46

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,785
Website

Re: 4 kissing circles

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

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#6 2012-11-22 01:38:45

bob bundy
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Registered: 2010-06-20
Posts: 6,528

Re: 4 kissing circles

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

Bob


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

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#7 2013-01-22 04:15:01

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

Re: 4 kissing circles

Did you steal my idea? eek faint


- n872yt3r
Math Is Fun Rocks! smile
By the power of the exponent, I square and cube you! cool

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#8 2013-01-22 04:49:24

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

Re: 4 kissing circles

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

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#9 2013-01-25 15:06:27

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,785
Website

Re: 4 kissing circles

Hi n872yt3r.
WHAT ARE YOU TALKING ABOUT?


'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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#10 2013-01-25 23:26:12

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

Re: 4 kissing circles

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

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