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#1 2012-11-22 14:00:35
- Agnishom
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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
Last edited by Agnishom (2012-11-22 14:03:47)
'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'
'The whole person changes, why can't a habit?' -65
#3 2012-11-23 00:17:48
- Agnishom
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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'
'The whole person changes, why can't a habit?' -65
#4 2012-11-23 00:28:51
- bob bundy
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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
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
#5 2012-11-23 00:36:46
- Agnishom
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Re: 4 kissing circles
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'
'The whole person changes, why can't a habit?' -65
#9 2013-01-26 14:06:27
- Agnishom
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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'
'The whole person changes, why can't a habit?' -65
#10 2013-01-26 22:26:12
- n872yt3r
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Re: 4 kissing circles
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!
