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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: 17,139
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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)


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

bob bundy
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Registered: 2010-06-20
Posts: 6,421

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: 17,139
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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 made a human being happy! There is no further achievement.' -bobbym

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

bob bundy
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Registered: 2010-06-20
Posts: 6,421

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
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From: The Complex Plane
Registered: 2011-01-29
Posts: 17,139
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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 made a human being happy! There is no further achievement.' -bobbym

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

bob bundy
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Registered: 2010-06-20
Posts: 6,421

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
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Registered: 2013-01-21
Posts: 392

Re: 4 kissing circles

Did you steal my idea? eek faint


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Math Is Fun Rocks! smile
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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
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From: The Complex Plane
Registered: 2011-01-29
Posts: 17,139
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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 made a human being happy! There is no further achievement.' -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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