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**thedarktiger****Member**- Registered: 2014-01-10
- Posts: 91

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!

:D:D

Good. You can read.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,816

Hi thedarktiger;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,548

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

Children are not defined by school ...........The Fonz

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,816

Hi Bob;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,548

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.

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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,548

diagram

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

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,374

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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,548

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,816

Hi phrontister;

Nice video.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,374

Thanks, B&B!

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.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,548

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.

Bob

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

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**thedarktiger****Member**- Registered: 2014-01-10
- Posts: 91

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

Good. You can read.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,816

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.****If it ain't broke, fix it until it is.**

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,548

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,816

Hi;

I would have to agree.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,374

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,816

The Alpha and the Omega!

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**thedarktiger****Member**- Registered: 2014-01-10
- Posts: 91

so it is

Good. You can read.

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