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

Offline

### 4 kissing circles

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

Uploaded Images

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

Offline

### 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

Uploaded Images

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

Offline

### 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

Offline

### 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

Uploaded Images

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

Offline

### 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

Offline

### 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

Offline

### 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?' -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!

## Board footer

Powered by FluxBB