Question

if a is the center of the circle, then which statement explains how ed is related to fd? ed ≅ fd because ef is perpendicular to a radius of circle a. ed ≅ fd because ef ≅ gf. ed ≅ fd because the inscribed angles that create the segments are congruent.

Explanation:

Step1: Recall the perpendicular - bisector of a chord property

In a circle, if a radius (or a line from the center of the circle) is perpendicular to a chord, then it bisects the chord.
Here, \(A\) is the center of the circle and \(AD\perp EF\).

Step2: Apply the property to segment \(EF\)

Since \(AD\) is a line from the center \(A\) and \(AD\perp EF\), by the perpendicular - bisector of a chord property, \(ED = FD\) (i.e., \(\overline{ED}\cong\overline{FD}\))

Answer:

\(\overline{ED}\cong\overline{FD}\) because \(AD\) (a line from the center \(A\)) is perpendicular to chord \(EF\) and bisects it.