Final answer:
If the distance from the origin to a given point is greater than 6, then that point lies inside circle Q. Option C "If the distance from the origin to a given point is greater than 6, then that point lies inside circle Q" is correct.
Step-by-step explanation:
To understand why this statement is true, let's consider the properties of a circle. The distance from the center of a circle to any point on its circumference is called the radius. In this case, the radius of circle Q is given as 6.
Now, if the distance from the origin (the center of circle Q) to a given point is greater than 6, that means the point is outside the circle, beyond its circumference. This is because any point outside the circle will have a greater distance from the center (origin) than the radius.
On the other hand, if the distance from the origin to a given point is less than 6, that means the point is inside the circle. Any point inside the circle will have a distance from the center (origin) that is smaller than the radius.
If the distance from the origin to a given point is exactly 6, then that point lies on the circumference of circle Q. This is because the distance from the center to any point on the circle's circumference is equal to the radius.
In conclusion, option C is the correct statement. If the distance from the origin to a given point is greater than 6, then that point lies inside circle Q.