8.1.6 If Two Arcs of a Circle (or of Congruent Circles) are Congruent, then the Corresponding Chords are Equal.

8.1.6 If Two Arcs of a Circle (or of Congruent Circles) are Congruent, then the Corresponding Chords are Equal.

In the circle with centre $O$, $\widehat{APB} \cong \widehat{CQD}$ and $\overline{AB}$, $\overline{CD}$ are their corresponding chords, then $\overline{AB} \cong \overline{CD}$

[Diagram: congruent arcs $\widehat{APB}$, $\widehat{CQD}$ with chords $\overline{AB}$, $\overline{CD}$]

Example 8

In a circular garden, two pair of decorative lights are placed such that the arcs between each pair ($A$ and $B$, $C$ and $D$) are equal in length. If the straight-line distance between points $A$ and $B$ is $8$ metres, what is the distance points $C$ and $D$?

Solution Given that

Since the arcs $AB$ and $CD$ are congruent, so their chords must be equal.

Hence, $m\overline{CD} = 8$ m