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The circle below is center Ed at O. Decide which length,if any, is definitely the same as the length. a) AD. b) BC. Justify your answers
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2 Answers

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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].
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#a

AD

look AD is the radius of circle

- So it's equal to DF as DF is another radius .

Answer is DF

#b

No one

BC is a part of BE and intersected by OC which is not bisector

So no one is equal to BC .
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