Math Is Fun Forum

cooljackiec

Member

Registered: 2012-12-13

Posts: 186

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

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

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

---

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

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

---

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

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

---

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: tangents

Do you agree with Q3?

Yes!

Are you giving hints about how you did them? 

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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
The knowledge of some things as a function of age is a delta function.

cooljackiec

Member

Registered: 2012-12-13

Posts: 186

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: tangents

Second attempt at a diagram.

Is this correct?

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phanthanhtom

Member

Registered: 2012-06-22

Posts: 290

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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

Re: tangents

For the first problem I am getting

.

How did you get that? I tried it assuming the bigger circle's radius as R and the smaller one's as r, got stuck in r² + 36 = R².

---

Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.
May his adventurous soul rest in peace at heaven.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: tangents

hi Monox D. I-Fly

That's correct for the first step.  Then:

I'll leave you to finish this.

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

Re: tangents

Ugh... How did I overlook something this simple? It's only one step to boot...

---

Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.
May his adventurous soul rest in peace at heaven.