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

cooljackiec
Member
Registered: 2012-12-13
Posts: 162

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: 88,714

Re: circle lengths

Hi cooljackiec;


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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

cooljackiec
Member
Registered: 2012-12-13
Posts: 162

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: 6,466

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: 162

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: 6,466

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: 162

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: 88,714

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

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

cooljackiec
Member
Registered: 2012-12-13
Posts: 162

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: 88,714

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

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

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,466

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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