# area of a circle in a square

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• Feb 11th 2011, 10:13 AM
kitobeirens
area 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 AM
Wilmer
You forgot length of red line...
• Feb 11th 2011, 11:56 AM
kitobeirens
oh yeah sorry it is 6
• Feb 11th 2011, 11:56 AM
kitobeirens
i meant 6
• Feb 11th 2011, 12:25 PM
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 PM
kitobeirens
oh cheers archie, what would that make the area of the circle
• Feb 11th 2011, 12:30 PM
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 PM
kitobeirens
so what is r ?
• Feb 11th 2011, 12:35 PM
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 PM
kitobeirens
so r = 25 ??????????
• Feb 11th 2011, 12:40 PM
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 PM
kitobeirens
so the two numbers need to multiply to 45 and add to 18 so 15 and 3 again?
• Feb 11th 2011, 12:46 PM
Quote:

Originally Posted by kitobeirens
so the two numbers need to multiply to 45 and add to 18 so 15 and 3 again?

Yes, that's how the quadratic was factored.

Now the two factors in brackets give you the answers visually.

What is R-15 if R=15 and what is R-3 if R=3 ?
• Feb 11th 2011, 12:53 PM
Wilmer
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 PM
kitobeirens
oh its 15 isnt it because 15 squared =225 -(18x15=270) so 225-270+45=0
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