# Thread: Circle - System of inequalities

1. ## Circle - System of inequalities

A ring on an archery target is bounded by two circles of radii 2ft and 3ft, respectively. Suppose the origin is at the center of the target. Write a system of inequality whose solution is the ring.

Where do I start?

I know that an equation for a circle is $\displaystyle (x-h)^2 + (y-k)^2 = r^2$

So would the inequality be $\displaystyle x^2 + y^2 < 4$ and $\displaystyle x^2 + y^2 < 9$ ?

2. Hello, chrozer!

A ring on an archery target is bounded by two circles of radii 2ft and 3ft.
Suppose the origin is at the center of the target.
Write a system of inequality whose solution is the ring.
You were quite close . . .

The ring is the area outside of the smaller circle, $\displaystyle x^2+y^2 \:=\:4$
. . and inside the larger circle, $\displaystyle x^2+y^2 \:=\:9$

So we want: .$\displaystyle \begin{Bmatrix}x^2+y^2 & > & 4 \\ x^2+y^2 & < & 9 \end{Bmatrix}$

If the circles themselves are included as part of the ring,
. . then we'll use $\displaystyle \geq$ and $\displaystyle \leq.$

3. Originally Posted by Soroban
Hello, chrozer!

You were quite close . . .

The ring is the area outside of the smaller circle, $\displaystyle x^2+y^2 \:=\:4$
. . and inside the larger circle, $\displaystyle x^2+y^2 \:=\:9$

So we want: .$\displaystyle \begin{Bmatrix}x^2+y^2 & > & 4 \\ x^2+y^2 & < & 9 \end{Bmatrix}$

If the circles themselves are included as part of the ring,
. . then we'll use $\displaystyle \geq$ and $\displaystyle \leq.$

Ok. I see....thanx alot.