Answer:
Point O is the center of the circle.
Part (a)
[tex]\overline{A\:\!F}[/tex] is a chord.
[tex]\overline{OD}[/tex] is a segment of the radius and is perpendicular to [tex]\overline{A\:\!F}[/tex]
If a radius is perpendicular to a chord, it bisects the chord (divides the chord into two equal parts).
Therefore, [tex]\overline{AD}=\overline{DF}[/tex]
Part (b)
If [tex]\overline{BE}[/tex] was extended past point E to touch the circumference it would be a chord.
As [tex]\overline{OC}[/tex] is perpendicular to [tex]\overline{BE}[/tex], it would bisect the chord, but as [tex]\overline{BE}[/tex] is only a portion of a chord, [tex]\overline{OC}[/tex] does not bisect [tex]\overline{BE}[/tex].
Therefore, there is no length equal to [tex]\overline{BC}[/tex].
