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Agnishom
2013-03-17 15:06:15

Thank you

Nehushtan
2013-03-17 03:09:30

Here you go.

Agnishom
2013-03-16 12:54:42

Please upload a diagram, I really do not understand from "Applying Pythagoras Theorem..."

Agnishom
2013-03-15 18:18:18

Thanks Nehushtan
I shall ask you if I have any doubts

bobbym
2013-03-15 17:19:41

Hi Agnishom;

Thanks for the drawing.

Nehushtan
2013-03-15 13:45:43

#### Agnishom wrote:

This is what I got.

Let
be the centre of
and
the point of contact of
with
. Let
be the centre of
and
the point of contact of
with
.

Let
be the point on
such that
is a rectangle. Applying Pythagoras’s theorem to
gives
.

Let
be the point on
such that
is a rectangle. Applying Pythagoras’s theorem to
gives
.

Let
be the point on
such that
is a rectangle. Applying Pythagoras’s theorem to
gives
.

Then

Hence:

Agnishom
2013-03-15 13:12:12

This is the only diagram I can imagine.

A rough sketch though...

1001 Words ≈ 7 KB
1 picture > 100 KB

Obviously, a picture is worth more....

Agnishom
2013-03-15 12:59:39

Bob, if you want I can give a diagram

bobbym
2013-03-15 09:42:50

Hi Agnishom;

#### bobbym wrote:

A picture is worth a thousand words.

For people like me who are geometrically challenged this problem is a nightmare. So far I have come up with 10^16 different possible drawings that to me fit those constraints.

Now I am busy looking up externally tangent, internally tangent, tangerine tangent... in the hopes of what externally tangent to the line means. Intersects at one point?

I see that bob has got his circles with their centers on the line, I have lifted my circles and it was hard to do, after all there are an infinite amount of them, to roll on the line. That takes care of externally tangent. Now this second bunch of circles, where do they go?

#### John McCarthy wrote:

As the Chinese say, 1001 words is worth more than a picture.

Maybe I shouldn't need the diagram...

anonimnystefy
2013-03-15 07:05:57

I am getting 1/2.

bob bundy
2013-03-15 04:07:38

hi Agnishom,

I'm not getting this yet.  I've drawn a line L .  Now it says 'on a straight line l' so I assumed that the circles had their centres on the line, and that each circle touches the ones on either side of it.  That covers the 'externally tangential to circle(n-1) and circle(n+1) but apparently also tangential to L itself.  How does that happen?  And I haven't even got to the second sentence yet.

Bob

Agnishom
2013-03-15 03:32:52

bobbym
2013-02-12 01:07:24

Please hold on the latex maker is not holding up, I am aware of that and am editing the original post.

All done!

anonimnystefy
2013-02-12 01:03:23

Hi bobbym

$\frac{\ln{\left (1+\frac{2}{3} \right )}}{1-\frac{2}{3}}\neq \ln{5}$

Agnishom
2013-02-12 00:54:28

Let me try it out