Question

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

Answer 1

Answer:

Point O is the center of the circle.

Part (a)

$\overline{A\:\!F}$ is a chord.

$\overline{OD}$ is a segment of the radius and is perpendicular to  $\overline{A\:\!F}$

If a radius is perpendicular to a chord, it bisects the chord (divides the chord into two equal parts).

Therefore, $\overline{AD}=\overline{DF}$

Part (b)

If $\overline{BE}$ was extended past point E to touch the circumference it would be a chord.

As $\overline{OC}$ is perpendicular to $\overline{BE}$,  it would bisect the chord, but as $\overline{BE}$ is only a portion of a chord, $\overline{OC}$ does not bisect $\overline{BE}$.

Therefore, there is no length equal to $\overline{BC}$.