Inscribed Circles
A circle with center _O_ is inscribed in square _ABCD_, which has a perimeter of 40.
| Quantity A | Quantity B |
|----|----|
| _y_ | 0 |
Incorrect.
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_y_ is not necessarily a positive number. Try starting by setting 2_x_ + 3 equal to the radius so you can solve for _x_.
Correct.
If square _ABCD_ has a perimeter of 40, each side has a length of 10. The radius of an inscribed circle is half the length of a side, so the radius is 5.
You can use this length to solve for _x_.
$$\displaystyle 2x + 3=5$$
$$\displaystyle x=1$$
Now that you know _x_, you can solve for _y_.
$$\displaystyle 5=6x + 4y=6(1) + 4y=6 + 4y$$
$$\displaystyle 4y + 6=5$$
$$\displaystyle 4y=-1$$
$$\displaystyle y=-\frac{1}{4}$$
$$\displaystyle y<0$$
Incorrect.
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The two line segments intersecting at _O_ are radii of the circle and have the same length. Try starting by setting 2_x_ + 3 equal to the radius so you can solve for _x_.
Incorrect.
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After you calculate the radius of the circle, you can use it to solve for _x_, and then for _y_.
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
