# Math Help - area of a circle in a square

1. ## 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...

2. You forgot length of red line...

3. oh yeah sorry it is 6

4. i meant 6

5. You could use Pythagoras' theorem

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

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

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

$(R-3)(R-15)=0$

6. oh cheers archie, what would that make the area of the circle

7. Now that you get R (the smart choice from the factors), plug it into the circle area formula

$A={\pi}R^2$

8. so what is r ?

9. 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.

10. so r = 25 ??????????

11. 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 ?

12. so the two numbers need to multiply to 45 and add to 18 so 15 and 3 again?

13. 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 ?

14. 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.

15. oh its 15 isnt it because 15 squared =225 -(18x15=270) so 225-270+45=0

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