The key is the rectangle region on the basketball court from the free throw line to the backboard. The backboard is 4 feet from the baseline. The key is 12 feet by 19 feet with a composite circle as the free throw line. Is the key similar to the basketball court? Is the inner circle similar to the entire circle in the center of the court? Explain both questions?
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To determine whether the key is similar to the basketball court, we need to compare their corresponding sides. The key is defined as a rectangle region on the basketball court, so we will compare the length and width of the key to the length and width of the entire basketball court.
The key is described as 12 feet by 19 feet, which means its length is 12 feet and its width is 19 feet. On the other hand, the size of a basketball court varies, but the standard NBA court has a length of 94 feet and a width of 50 feet.
Comparing the sides, we find that the key's length is much smaller than the length of the basketball court (12 feet versus 94 feet). Similarly, the key's width is also smaller than the width of the basketball court (19 feet versus 50 feet). Therefore, we can conclude that the key is not similar to the basketball court since their corresponding sides have different lengths.
Moving on to the inner circle, we need to compare it to the entire circle in the center of the court. The inner circle in the key is referred to as the free throw circle, which is also a composite circle. To determine similarity, we again need to compare their corresponding parts.
The composite circle in the key has a radius equal to the free throw line's distance from the backboard. Given that the backboard is 4 feet from the baseline, we can calculate the radius as the distance from the free throw line to the baseline, which is half the key's width or half of 19 feet, roughly 9.5 feet.
On the other hand, the entire circle in the center of the court is typically known as the "center circle" or "jump circle." It has a standard radius of 6 feet in the NBA.
Comparing the radii, we find that the radius of the inner circle in the key (9.5 feet) is greater than the radius of the entire circle in the center of the court (6 feet). Therefore, we can conclude that the inner circle is not similar to the entire circle in the center of the court.
In summary, neither the key nor the inner circle are similar to the entire basketball court. The key is smaller in size compared to the court, while the inner circle has a larger radius than the entire circle in the center of the court.