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#1 2013-06-25 11:13:18

cooljackiec
Member
Registered: 2012-12-13
Posts: 160

circle lengths

In the adjoining figure,  AB is tangent at  A to the circle with center O , point D is interior to the circle, and DB intersects the circle at C. If BC = DC = 3,OD = 2 , and AB = 6, then find the radius of the circle.

View Image: ScreenHunter_237 Jun. 25 16.13.jpg

I see you have graph paper.
You must be plotting something
lol

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#2 2013-06-25 13:18:25

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,238

Re: circle lengths

Hi cooljackiec;


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#3 2013-06-27 05:04:30

cooljackiec
Member
Registered: 2012-12-13
Posts: 160

Re: circle lengths

thanks. can you help me on this?

View Image: ScreenHunter_01 Jun. 27 09.37.gif

I see you have graph paper.
You must be plotting something
lol

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#4 2013-06-27 05:29:02

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,426

Re: circle lengths

hi

There's a theorem that is true for all circles.  For any four points on the circumference, see diagram

AE x EC = DE x EB

That should be enough for you to do this one.

Bob

ps.  to prove it look for equal angles using the circle theorems and then similar triangles.

View Image: cooljackiec5.gif

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

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#5 2013-06-27 07:31:35

cooljackiec
Member
Registered: 2012-12-13
Posts: 160

Re: circle lengths

hmm.. that is the power of a point theorem right?? i think it works for secants/tagents too


I see you have graph paper.
You must be plotting something
lol

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#6 2013-06-27 09:46:47

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,426

Re: circle lengths

I've not met it called that, but Wiki agrees with you:

http://en.wikipedia.org/wiki/Power_of_a_point

And yes it does apply to tangents.

Bob


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

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#7 2013-06-27 11:24:55

cooljackiec
Member
Registered: 2012-12-13
Posts: 160

Re: circle lengths

still stuck sad


I see you have graph paper.
You must be plotting something
lol

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#8 2013-06-27 12:37:33

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,238

Re: circle lengths

Hi;

I got an answer of 31 by another method. Can you check it?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#9 2013-06-27 14:20:44

cooljackiec
Member
Registered: 2012-12-13
Posts: 160

Re: circle lengths

seems correct. how did you do that?


I see you have graph paper.
You must be plotting something
lol

Offline

#10 2013-06-27 14:27:38

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,238

Re: circle lengths

I have been experimenting with the team of bobbym and geogebra, trying to be more than an amazed bystander. The great gAr would describe it as a "mathod!"


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#11 2013-06-27 19:20:01

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,426

Re: circle lengths

hi cooljackiec

still stuck

I'm assuming you mean with the question in post 3.

I put x = XP and y = QY.

Then applied the theorem twice:

5 x 6 = x(27+y)
7 x 12 = (x+27)y

I subtracted to eliminate xy.

Then made y the subject of that and substituted back into one equation to make a quadratic.

It factorised easily with one positive and one negative root.  Rejected the negative and then substituted back to find y.

Got the same answer as bobbym.  smile

Bob


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

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