# Weekly Math Problem

## Weekly Math Problem

Weekly Math Problem

As of Saterday the 24 th of April i will be posting weekly math problems

the answers will be due by Sat 12:00 am of the following week

The answers will be PM'ed to me with explanations.

Any questions about the problem should be asked on this post so it can benifit everyone

Winners will be announced here

As of Saterday the 24 th of April i will be posting weekly math problems

the answers will be due by Sat 12:00 am of the following week

The answers will be PM'ed to me with explanations.

Any questions about the problem should be asked on this post so it can benifit everyone

Winners will be announced here

**i4sci**- Academic Moderator
- Posts : 87

Join date : 2010-04-13

Location : under a rock

## Re: Weekly Math Problem

hi dan

**zangetsuosan**- Member
- Posts : 37

Join date : 2010-04-23

Age : 23

Location : In your attic :D

## Re: Weekly Math Problem

I m changing the questions to monday cuz my Sundays are going to be busier than i thought

Find the formula for finding the Area of an n-gon with a circle inscribed in it

the only known is the radius of the inscirbed circle.

Find the formula for finding the Area of an n-gon with a circle inscribed in it

the only known is the radius of the inscirbed circle.

**i4sci**- Academic Moderator
- Posts : 87

Join date : 2010-04-13

Location : under a rock

## Re: Weekly Math Problem

OK

A is the area of the polygon+ the area of the inscribed circle.

F is the area of the circle.

C is the final area

C=A-F

Just logic =D

A is the area of the polygon+ the area of the inscribed circle.

F is the area of the circle.

C is the final area

C=A-F

Just logic =D

_________________

"Noli confuta sine agone"

Never give up without a fight

~Ali

I am a Muslim, and proud of it!

**LGBT = BAD**

MUSIC = BAD

MUSIC = BAD

## Re: Weekly Math Problem

no i need a more specific equation

btw the polygon is perfect

btw the polygon is perfect

**i4sci**- Academic Moderator
- Posts : 87

Join date : 2010-04-13

Location : under a rock

## Re: Weekly Math Problem

nice question dan

**zangetsuosan**- Member
- Posts : 37

Join date : 2010-04-23

Age : 23

Location : In your attic :D

## Re: Weekly Math Problem

I must admit, I am completely stumped. I have no idea.

_________________

"Noli confuta sine agone"

Never give up without a fight

~Ali

I am a Muslim, and proud of it!

**LGBT = BAD**

MUSIC = BAD

MUSIC = BAD

## Re: Weekly Math Problem

Commander Ali wrote:I must admit, I am completely stumped. I have no idea.

perhaps you should noli confuta sine agonem, Commander

**i4sci**- Academic Moderator
- Posts : 87

Join date : 2010-04-13

Location : under a rock

## Re: Weekly Math Problem

How about you give me a hint?

_________________

"Noli confuta sine agone"

Never give up without a fight

~Ali

I am a Muslim, and proud of it!

**LGBT = BAD**

MUSIC = BAD

MUSIC = BAD

**i4sci**- Academic Moderator
- Posts : 87

Join date : 2010-04-13

Location : under a rock

## Re: Weekly Math Problem

Ok, so the answer to my question is An = (n/2)*r^2 * sin(180/n)

so if i split up the entire polygon into n triangles, with the sides coming from the center and meeting and the vertexes, which would make them equal to r the radius of the inscribed circle. thus the area of the polygon would be n times the area of all those triangles.

The area of a triangle, as we all should hopeful know, is the base times the height all over two. To find the height and base we use simple trigonometry. The angle between the two radii would be 360/n. thus the height would be r*cos 180/n and the base would be 2r* sin 180/n. Multiplying them together will yield r^2 * cos (180/n) * sin *(180/n). Now, we must not for get our hand trigonometric identities, that help us in times such as these. It just so happens that sin x * cos x = sin 2x/2. Thus, our final equation becomes A = n/2 * r^2 * sin (360/n).

so if i split up the entire polygon into n triangles, with the sides coming from the center and meeting and the vertexes, which would make them equal to r the radius of the inscribed circle. thus the area of the polygon would be n times the area of all those triangles.

The area of a triangle, as we all should hopeful know, is the base times the height all over two. To find the height and base we use simple trigonometry. The angle between the two radii would be 360/n. thus the height would be r*cos 180/n and the base would be 2r* sin 180/n. Multiplying them together will yield r^2 * cos (180/n) * sin *(180/n). Now, we must not for get our hand trigonometric identities, that help us in times such as these. It just so happens that sin x * cos x = sin 2x/2. Thus, our final equation becomes A = n/2 * r^2 * sin (360/n).

**i4sci**- Academic Moderator
- Posts : 87

Join date : 2010-04-13

Location : under a rock

## Re: Weekly Math Problem

Whats the next one?

_________________

"Noli confuta sine agone"

Never give up without a fight

~Ali

I am a Muslim, and proud of it!

**LGBT = BAD**

MUSIC = BAD

MUSIC = BAD

## Re: Weekly Math Problem

Ok, with the unending problem that i have with the Dell Mini 12, i have problems accessing the forum. This is the reason for the delay. But anyways Here is the problem for this week ( Due Sunday 12:00 PM Eastern Time, PM me the answers And the explanations).

The known are R and r, the radii of the two circles and the angle, theta, must be found, obviously in terms of R and r. Lines AO and BO are tangent to the two circles. The two circles also touch at one point

THEY DO NOT CROSS OVER!!!!!!!!!!!!.

Diagram ( please excuse of the crudity of this, i was using paint and it sucks ****)

https://i.servimg.com/u/f66/15/16/53/62/proble10.jpg

The known are R and r, the radii of the two circles and the angle, theta, must be found, obviously in terms of R and r. Lines AO and BO are tangent to the two circles. The two circles also touch at one point

THEY DO NOT CROSS OVER!!!!!!!!!!!!.

Diagram ( please excuse of the crudity of this, i was using paint and it sucks ****)

https://i.servimg.com/u/f66/15/16/53/62/proble10.jpg

**i4sci**- Academic Moderator
- Posts : 87

Join date : 2010-04-13

Location : under a rock

## Re: Weekly Math Problem

Is X the whole tangent, or just a part?

_________________

"Noli confuta sine agone"

Never give up without a fight

~Ali

I am a Muslim, and proud of it!

**LGBT = BAD**

MUSIC = BAD

MUSIC = BAD

## Re: Weekly Math Problem

Commander Ali wrote:Is X the whole tangent, or just a part?

Its from the point where r touches the tangent to point O

**i4sci**- Academic Moderator
- Posts : 87

Join date : 2010-04-13

Location : under a rock

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