text: Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °
  
  You are not logged in.
  
  ## #1 2012-11-22 14:00:35
  
  Agnishom
  Real Member
  
  Online
  
  ### 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?' -Alokananda
  
  ## #2 2012-11-22 20:03:24
  
  bob bundy
  Moderator
  
  Online
  
  ### 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
  
  You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
  
  ## #3 2012-11-23 00:17:48
  
  Agnishom
  Real Member
  
  Online
  
  ### 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?' -Alokananda
  
  ## #4 2012-11-23 00:28:51
  
  bob bundy
  Moderator
  
  Online
  
  ### 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
  Real Member
  
  Online
  
  ### 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?' -Alokananda
  
  ## #6 2012-11-23 00:38:45
  
  bob bundy
  Moderator
  
  Online
  
  ### 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
  
  ## #7 2013-01-23 03:15:01
  
  n872yt3r
  Power Member
  
  Offline
  
  ### Re: 4 kissing circles
  
  Did you steal my idea?
  
  - n872yt3r
  Math Is Fun Rocks!
  By the power of the exponent, I square and cube you!
  
  ## #8 2013-01-23 03:49:24
  
  n872yt3r
  Power Member
  
  Offline
  
  ### 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!
  By the power of the exponent, I square and cube you!
  
  ## #9 2013-01-26 14:06:27
  
  Agnishom
  Real Member
  
  Online
  
  ### Re: 4 kissing circles
  
  Hi n872yt3r.
  
  '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?' -Alokananda
  
  ## #10 2013-01-26 22:26:12
  
  n872yt3r
  Power Member
  
  Offline
  
  ### 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!
explanation: The text extract is a discussion thread from a math forum, where a user named Agnishom posts a math problem involving the radii of four kissing circles. Another user, bob bundy, provides a solution using geometric principles. The discussion continues with Agnishom asking for further clarification, and bob bundy providing additional details.
  
  The document contains a math question and an answer to this question.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °
  
  You are not logged in.
  
  ## #1 2012-11-22 14:00:35
  
  Agnishom
  Real Member
  
  Online
  
  ### 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?' -Alokananda
  
  ## #2 2012-11-22 20:03:24
  
  bob bundy
  Moderator
  
  Online
  
  ### 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
  
  You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
  
  ## #3 2012-11-23 00:17:48
  
  Agnishom
  Real Member
  
  Online
  
  ### 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?' -Alokananda
  
  ## #4 2012-11-23 00:28:51
  
  bob bundy
  Moderator
  
  Online
  
  ### 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
  Real Member
  
  Online
  
  ### 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?' -Alokananda
  
  ## #6 2012-11-23 00:38:45
  
  bob bundy
  Moderator
  
  Online
  
  ### 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
  
  ## #7 2013-01-23 03:15:01
  
  n872yt3r
  Power Member
  
  Offline
  
  ### Re: 4 kissing circles
  
  Did you steal my idea?
  
  - n872yt3r
  Math Is Fun Rocks!
  By the power of the exponent, I square and cube you!
  
  ## #8 2013-01-23 03:49:24
  
  n872yt3r
  Power Member
  
  Offline
  
  ### 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!
  By the power of the exponent, I square and cube you!
  
  ## #9 2013-01-26 14:06:27
  
  Agnishom
  Real Member
  
  Online
  
  ### Re: 4 kissing circles
  
  Hi n872yt3r.
  
  '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?' -Alokananda
  
  ## #10 2013-01-26 22:26:12
  
  n872yt3r
  Power Member
  
  Offline
  
  ### 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!
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The text extract is a discussion thread from a math forum, where a user named Agnishom posts a math problem involving the radii of four kissing circles. Another user, bob bundy, provides a solution using geometric principles. The discussion continues with Agnishom asking for further clarification, and bob bundy providing additional details.
  
  The document contains a math question and an answer to this question.
  
  Label: question-and-answer