i have been given a question and i don't know how to work it out please help. green line is 3 cm and red line is cm the circle is supposed to just be touching the square, i might have put something wrong but it is about this help...

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- Feb 11th 2011, 10:13 AMkitobeirensarea of a circle in a square
i have been given a question and i don't know how to work it out please help. green line is 3 cm and red line is cm the circle is supposed to just be touching the square, i might have put something wrong but it is about this help...

Attachment 20753 - Feb 11th 2011, 11:53 AMWilmer
You forgot length of red line...

- Feb 11th 2011, 11:56 AMkitobeirens
oh yeah sorry it is 6

- Feb 11th 2011, 11:56 AMkitobeirens
i meant 6

- Feb 11th 2011, 12:25 PMArchie Meade
You could use Pythagoras' theorem

$\displaystyle R^2=(R-6)^2+(R-3)^2$

$\displaystyle R^2=R^2-12R+36+R^2-6R+9$

$\displaystyle R^2-18R+45=0$

$\displaystyle (R-3)(R-15)=0$ - Feb 11th 2011, 12:28 PMkitobeirens
oh cheers archie, what would that make the area of the circle

- Feb 11th 2011, 12:30 PMArchie Meade
Now that you get R (the smart choice from the factors), plug it into the circle area formula

$\displaystyle A={\pi}R^2$ - Feb 11th 2011, 12:33 PMkitobeirens
so what is r ?

- Feb 11th 2011, 12:35 PMArchie Meade
Have a think about it.

The background to this is being able to factor a quadratic

and discover the solution of the radius from the factors.

Then use the radius to calculate circle area.

You need to know this. - Feb 11th 2011, 12:38 PMkitobeirens
so r = 25 ??????????

- Feb 11th 2011, 12:40 PMArchie Meade
You didn't think for very long !

Have a look at the factors.

When you multiply them, the answer is zero.

So, either factor is zero for a certain value of R.

What values of R make those factors 0 ? - Feb 11th 2011, 12:44 PMkitobeirens
so the two numbers need to multiply to 45 and add to 18 so 15 and 3 again?

- Feb 11th 2011, 12:46 PMArchie Meade
- Feb 11th 2011, 12:53 PMWilmer
Kito, since you obviously don't understand how the quadratic formula works,

then you are not ready for this problem. Suggest you talk to your math teacher. - Feb 11th 2011, 12:57 PMkitobeirens
oh its 15 isnt it because 15 squared =225 -(18x15=270) so 225-270+45=0