Question

The circle below is centred at O. Decide which length, if any, is definitely the same as the length a) AD. b) BC. Justify your answers. A B E Not drawn accurately Answer>​

Answer 1

a. A length that is definitely the same as the length AD is line DF.

b. There is definitely no length that is the same as the length BC.

In Mathematics and Geometry, the chord of a circle is a line segment that join any two (2) points on a circle. This ultimately implies that, a chord simply refers to the section of the line that is used for connecting two separate points on a circle.

Part a.

By critically observing circle O, we can logically deduce that line A F is a chord. Also, the radius of this circle is OD and it is perpendicular to line A F. Hence, the radius OD would bisect the chord into two equal parts;

`\overline {AD} =\overline {DF}`

Part b.

Assuming line BE is extended beyond point E and it touches the circumference of this circle, it would form a chord. Also, line OC would bisect the chord when it is perpendicular to line BE.

In the context of the diagram, line OC does not bisect line BE, so congruent sides are formed.