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#1 2013-06-17 05:57:49

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

tangents

i need help with some tangent/circle problems

Two circles have the same center. A chord of the larger circle is tangent to the smaller circle. If the length of the chord is 12, then find the area of the region inside the larger circle but outside the smaller circle.



The circular table in the diagram is pushed tangent to two perpendicular walls. The distances from  on the circumference to the two walls are 27 and 6. What is the radius of the table?


Given regular pentagon ABCDE , a circle can be drawn that is tangent to DC at D and to AB at A. What is the number of degrees in minor arc AD?

Points B and A are on a circle with center at O, and point P is outside the circle such that PA and PB are tangent to the circle. Find AB if PA=12 and the radius of the circle is 9.


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

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#2 2013-06-17 06:03:00

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: tangents

Hi


For the first problem I am getting
.

For the third problem I am getting

.

For the fourth problem, I am getting

.

Last edited by anonimnystefy (2013-06-17 06:14:00)


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#3 2013-06-17 06:12:31

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

Re: tangents

hi Stefy,

I've got Q3.  Cannot understand Q2 at all.  I have four points in a square and that's all.  ??

Bob


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

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#4 2013-06-17 06:16:36

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: tangents

Hi Bob

I have Q3 as well, I was just doing them out of order.

I cannot understand Q2 either. Mazbe we need to see the mentioned diagram to understand what's going on?

Last edited by anonimnystefy (2013-06-17 06:16:58)


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#5 2013-06-17 06:18:53

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

Re: tangents

Hi

I agree with both your answers.

Yes, a diagram would help.

I'll post a picture of what I am getting from the Q and maybe cooljackiec can correct it.

Bob


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

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#6 2013-06-17 06:24:23

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: tangents

Do you agree with Q3?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#7 2013-06-17 06:25:17

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

Re: tangents

hi cooljackiec

Q2 has stumped us at the moment.  I've made a diagram with a circular table against two walls.  The walls are AB and AD.

We know that the angle at A is 90; and so are the angles at B and D as the walls make tangents.

So ABCD is a square.

So where does the 27 and 6 come from?

Bob

View Image: coolwall.gif

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

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#8 2013-06-17 06:26:43

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

Re: tangents

Stefy wrote:

Do you agree with Q3?

Yes!

Are you giving hints about how you did them?  smile

Bob


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

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#9 2013-06-17 06:55:41

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

Re: tangents

Hi cooljackiec;


For Q2:

The circular table in the diagram is pushed tangent to two perpendicular walls. The distances from  on the circumference to the two walls are 27 and 6. What is the radius of the table?

r = 51 and r = 15

we reject r = 15 so the answer is r = 51.


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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#10 2013-06-17 09:51:14

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: tangents

Ah, I think I have it. 27 and 6 are the distances of on of the points on the circumference of the table. Figured it out from bobbym's equation. Good job on figuring it out, bobbym!


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#11 2013-06-17 10:03:59

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

Re: tangents

it was correct.

i was also stumped about 27 and 6. the diageam was corect


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

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#12 2013-06-17 18:55:08

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

Re: tangents

Second attempt at a diagram.

Is this correct?

Bob

View Image: coolwall.gif

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

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#13 2013-06-17 20:14:33

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

Re: tangents

Hi Bob;

This is what I drew. Circle center on y = x, Circle intersects (6,27) or (27,6). Tangent to the x and y axis.

View Image: 2013-06-18_005750.gif

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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#14 2013-06-17 21:17:01

phanthanhtom
Member
Registered: 2012-06-22
Posts: 215

Re: tangents

How old is this guy? This corresponds to VN grade 9. The teacher forces my grade 6 son to read the grade 9 textbook. Now he can do it. It looks obvious.

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#15 2013-06-17 21:39:21

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

Re: tangents

It looks obvious.

It can only be considered obvious if one is willing to accept my interpretaion of it as in post #13.

You see the question is incomplete. It is missing some words.

distances from  on the circumference

between "from" and "on" there is an important phrase missing. This is the confusion!


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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#16 2013-06-17 21:41:40

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: tangents

Hi bobbym

If we interpreted the wording correctly (and I believe we have) then I agree with your answer.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#17 2013-06-17 21:49:28

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

Re: tangents

I agree with his answer too. But the only reason that question did not fall in post #7 was because of the omitted words.


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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#18 2013-06-17 21:56:41

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: tangents

Yes, the wording was the cause of the problem.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#19 2013-06-17 22:00:59

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

Re: tangents

If everybody who posts questions would only learn the simple thing of being accurate they would come away with more than if they learned 100 theorems.


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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