In various constructions, you need to use the longer of two segments to construct the radius of a circle. Why do you think this is? What happens if you use the shorter segment?

construction such as?

Constructions with technology

I know this was 5 years ago bu i also need the answer to the same question!!

it is almost 10 years

The reason you need to use the longer of two segments to construct the radius of a circle is because the radius is defined as the distance from the center of the circle to any point on its circumference. If you use the shorter segment, you would not be measuring the true distance between the center and the circumference.

To understand this concept, let's consider a circle with two points, A and B, on its circumference. If you connect these two points with a straight line segment, called AB, the midpoint of this line segment will always lie on the circle's center. This midpoint can be found by drawing a perpendicular bisector, which bisects AB at a 90-degree angle.

Now, if you have two segments, AC and BC, each connecting the center of the circle with points A and B on the circumference, respectively, one of these segments will always be longer than the other. This can be proven using the Triangle Inequality Theorem, which states that in any triangle, the sum of the lengths of any two sides is always greater than the length of the third side.

If you were to use the shorter segment, say AC, as the radius of the circle, then you would not be accurately determining the distance from the center to the circumference. In fact, you would only be measuring the distance from the center to point A, which is not the true radius. Using the shorter segment would result in an incorrect representation of the circle and its properties.

Therefore, to properly construct the radius of a circle, you must always use the longer segment connecting the center with any point on the circumference. This ensures that the radius accurately represents the distance from the center to any point on the circle.