What is the method for determining the perimeter of a square inscribed in a circle, given the diameter of the circle (4 cm)?

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- Jul 19th 2006, 02:21 PMzosoSquare inscribed in circle...
What is the method for determining the perimeter of a square inscribed in a circle, given the diameter of the circle (4 cm)?

- Jul 19th 2006, 03:02 PMQuickQuote:

Originally Posted by**zoso**

$\displaystyle P_{square}=4s$

$\displaystyle d^2=s^2+s^2$

$\displaystyle d=\frac{c}{\pi}$

therefore...

$\displaystyle d^2=2s^2\Longrightarrow\sqrt{\frac{d^2}{2}=s$

substitute: $\displaystyle \sqrt{\left(\frac{c}{\pi}\right)^2\div2}}=s$

$\displaystyle \sqrt{\frac{c^2}{\pi^2}\times \frac{1}{2}}=s$

$\displaystyle \sqrt{\frac{c^2}{2\pi^2}}=s$

$\displaystyle \frac{c}{\pi\sqrt{2}}=s$

therefore

$\displaystyle \frac{4c}{\pi\sqrt{2}}=4s=P_{square}$

rationalize the denominator:$\displaystyle \frac{4c\sqrt{2}}{2\pi}=P_{square}$

Hello, you've discovered my hidden text! hurray for you!

~ $\displaystyle Q\!u\!i\!c\!k$ - Jul 19th 2006, 06:24 PMmalaygoelQuote:

The diameter of the circle is the length from one corner of the square to the opposite corner,

Why the above condition has to be true?

How many squares of different area can be inscribed in the circle? Why?

How many squares of different perimeter can be inscribed in the circle? Why?

Keep Smiling

Malay - Jul 19th 2006, 06:35 PMQuickQuote:

Originally Posted by**malaygoel**

Quote:

How many squares of different area can be inscribed in the circle? Why?

How many squares of different perimeter can be inscribed in the circle? Why?

Keep Smiling

Malay

- Jul 19th 2006, 06:42 PMmalaygoelQuote:

It's possible to have practically infinite squares inscribed in a circle, maybe if you set up a size restriction I could help you out more?

I think are misinterpreting the word 'inscribe'. I means that the vertices of the square lie on the circumference of the circle.

Quote:

Right, for Zoso ;) , the above condition is only true for the largest possible square you can inscribe in a circle. If that doesn't help I'll show Zoso a diagram.

The above condition is true because the vertex angle of square is 90 degrees.

Keep Smiling

Malay - Jul 19th 2006, 06:51 PMQuickQuote:

Originally Posted by**malaygoel**

**practically**infinite.

Quote:

There is no largest square, all of the inscibed squares have the same area.

The above condition is true because the vertex angle of square is 90 degrees.

Keep Smiling

Malay

as you can clearly see in the diagram, the diameter of the circle is the distance between two opposite corners of the square. - Jul 19th 2006, 07:36 PMThePerfectHacker
The diameter of the circle is the diagnol of the square.

- Jul 20th 2006, 11:35 AMzosoQuote:

Originally Posted by**Quick**

so if the diameter of the circle IS 4 cm, the result would be $\displaystyle 16\sqrt {2} cm$ or something near 22 cms for the perimeter? - Jul 20th 2006, 11:42 AMQuickQuote:

Originally Posted by**zoso**

$\displaystyle \frac{4c\sqrt{2}}{2\pi}=\frac{4(4)\sqrt{2}}{2\pi}= \frac{16\sqrt{2}}{2\pi}=\frac{8\sqrt{2}}{\pi}

\approx

3.601265265cm$ - Jul 20th 2006, 12:13 PMzoso
k, I see what I did wrong.

- Jul 21st 2006, 06:25 PMthedarktemplar
The diameter is 4cm...not the circumference. So, using pythagoras' theorem, 2 squard+ 2 sqard=8

root 8= 2.828

2.828 x 4= ~11.3 - Jul 21st 2006, 06:32 PMQuickQuote:

Originally Posted by**thedarktemplar**

Quote:

Originally Posted by**Quick**

$\displaystyle \frac{4d}{\sqrt{2}}=4s=P_{square}$