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#1 2014-02-02 22:34:02

thedarktiger
Member
Registered: 2014-01-10
Posts: 65

Triangles and tangents galore

Triangle ABC, inscribed in a circle, has AB = 15 and BC = 25. A tangent to the circle is drawn at B, and a line through A parallel to this tangent intersects \overline{BC} at D. Find DC.
This is weird. I tried stuff I know 'bout circles and triangles...(which is pretty close to nil)...but I can't get it.
Thanks!
big_smile:D:D


Good. You can read.

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#2 2014-02-02 23:23:05

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,980

Re: Triangles and tangents galore

Hi thedarktiger;


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#3 2014-02-03 21:17:46

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,268

Re: Triangles and tangents galore

Good morning bobbym,

Did you get that answer from geogebra or have you found a 'Euclidean' method.

I'm finding a solution to this one elusive at the moment.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#4 2014-02-03 21:24:42

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,980

Re: Triangles and tangents galore

Hi Bob;


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#5 2014-02-03 23:22:54

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,268

Re: Triangles and tangents galore

It's a strange problem.  There are an infinite number of triangles with those measurements.  I used Sketchpad to fix AB and then made a circle, centre B, for the locus of C.  Then I constructed the rest to find D.  As I move C, D moves around a circle of fixed radius, with a radius consistent with your answer for CD,  and centre B.  But why?

I seem to have landed up with two problems.  (i) Why is the locus for D a circle ? and (ii) what is its radius because once you know BD, you know DC.

??????

EDIT:  Oh how come I failed to see this earlier:

(cannot add a diagram to an edited post so I'll put in the next post )

angles EBA BCA and DAB are equal (angle props and parallels)

so

triangles DAB and ACB are similar

so AB/BD = CB/AB

I'll leave the rest to you.  smile

Bob

ps.  But why the red circle ?  working on that now.

No I'm not.  I've done it.  BD is fixed so D moves on a circle with that radius.

Last edited by bob bundy (2014-02-04 01:20:33)


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#6 2014-02-04 01:16:32

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,268

Re: Triangles and tangents galore

diagram

View Image: thedarktiger6.gif

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#7 2014-02-04 04:19:33

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,819

Re: Triangles and tangents galore

Here is a little video capture of my Geogebra program showing that DC's size remains constant at 16 when BC is pivoted 360° around point B.

Last edited by phrontister (2014-02-04 17:29:40)


"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#8 2014-02-04 05:03:14

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,268

Re: Triangles and tangents galore

Thanks Phro, that's lovely.  Like the music too.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#9 2014-02-04 07:50:47

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,980

Re: Triangles and tangents galore

Hi phrontister;

Nice video.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#10 2014-02-04 17:49:58

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,819

Re: Triangles and tangents galore

Thanks, B&B! smile

I've changed the link in that post to a longer version that oscillates, so that Bob can hear the whole song...which is The Engagement, apparently from an old movie, Silent Partner.

Just make sure that you're well-rested before viewing this one, or the hypnotic effect might getcha.

Watching the video, I imagine a huge albatross in flight. Maybe I could've used Fleetwood Mac's Albatross for the audio instead.


"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#11 2014-02-04 19:53:37

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,268

Re: Triangles and tangents galore

Thanks Phro,

That was very relaxing.  Yes, Fleetwood Mac would work well but, then again, I've got that one on vinyl so it was good to hear something new.

smile  smile  smile

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#12 2014-02-07 14:54:50

thedarktiger
Member
Registered: 2014-01-10
Posts: 65

Re: Triangles and tangents galore

Hmmm. Thanks for the demonstration phronstister! wow, It looks like geoebra is  amust


Good. You can read.

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#13 2014-02-07 15:23:27

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,980

Re: Triangles and tangents galore

Some old guy wrote:

Geogebra. geogebra, it is the man. If it can not do it, then nobody can! Yaaaaay, geogebra!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#14 2014-02-07 23:40:31

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,268

Re: Triangles and tangents galore

hi bobbym,

Can I make a claim for the first mention of geogebra on MIF ?

http://www.mathisfunforum.com/viewtopic … 01#p146001

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#15 2014-02-08 00:05:30

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,980

Re: Triangles and tangents galore

Hi;

I would have to agree.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#16 2014-02-08 00:06:09

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,819

Re: Triangles and tangents galore

And I'll make a claim for the most recent (to date) mention of geogebra on MIF. wink


"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#17 2014-02-08 00:07:19

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,980

Re: Triangles and tangents galore

The Alpha and the Omega!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#18 2014-02-08 16:30:35

thedarktiger
Member
Registered: 2014-01-10
Posts: 65

Re: Triangles and tangents galore

so it is big_smile


Good. You can read.

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