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

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

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,335

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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,335

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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,335

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

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: 6,335

Stefy wrote:

Do you agree with Q3?

Yes!

Are you giving hints about how you did them?

Bob

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,199

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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

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.

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

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

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,335

Second attempt at a diagram.

Is this correct?

Bob

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,199

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.

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

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,199

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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

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.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,199

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

Yes, the wording was the cause of the problem.

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,199

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.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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