Answer:
When the radius of a circle is increasing while the magnitude of a central angle is held constant, the length of the intercepted arc is also increasing.
To see why this is the case, let's consider the formula for the length of an arc, which is given by:
s = rθ
where s is the length of the intercepted arc, r is the radius of the circle, and θ is the central angle in radians.
If the radius is increasing but the magnitude of θ is held constant, then the length of the intercepted arc will increase as well. This is because s is directly proportional to r; as r increases, s will also increase.
To see this more concretely, imagine drawing a circle on a piece of paper with a certain radius and then drawing a central angle that intercepts a certain arc length. If we then increase the radius of the circle while keeping the central angle the same, the arc length will increase proportionally to the increase in radius. This is because the same central angle will now subtend a larger arc on the circle, since the circle is larger.
Therefore, when the radius of a circle is increasing while the magnitude of a central angle is held constant, the length of the intercepted arc is increasing as well.
Explanation: