Question

describe how you could change the location of point f on the circle without changing the value of m∠cfe. which of the following is a correct response? show hints f can be anywhere on (overset{\frown}{cef}). as long as the c and e are in the same location, the angle measure will remain the same. f can be anywhere on (overset{\frown}{ce}). as long as the c and e are in the same location, the angle measure will remain the same. f can be anywhere on (overset{\frown}{cfe}). as long as the c and e are in the same location, the angle measure will remain the same. the only other location f can be is at the mid - point of (overset{\frown}{ce}). if f is at any other point on the circle, the value of the angle will change.

Explanation:

The measure of an inscribed - angle in a circle is half of the measure of the intercepted arc. If points \(C\) and \(E\) remain fixed, the measure of the arc \(\overset{\frown}{CE}\) is fixed. The angle \(\angle CFE\) is an inscribed angle that intercepts the arc \(\overset{\frown}{CE}\). As long as \(C\) and \(E\) do not change, the measure of \(\angle CFE\) will not change for any point \(F\) on the arc \(\overset{\frown}{CFE}\) (the arc that has endpoints \(C\) and \(E\) and contains \(F\)).

Answer:

\(F\) can be anywhere on \(\overset{\frown}{CFE}\). As long as the \(C\) and \(E\) are in the same location, the angle measure will remain the same.