# In the circle shown below, AB = 3 and DE = 3. What is the value of z?

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Hint:- In a circle, we know that In the same circle or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.

Given, AB = 3 and DE = 3.

In the given circle, AB = DE and AB||DE. Hence, AB and DE are congruent chords of the circle.

And In a circle, or congruent circles, congruent chords have congruent arcs.

$

\because {\text{AB}} \cong {\text{DE}} \\

\therefore {\text{arc(AB) = arc(DE)}} \\

\Rightarrow {\text{ z = }}{90^ \circ } \\

$

Hence, the required answer is z = ${90^ \circ }$

Note:- In these types of questions, the key concept is the theorems of circles and chords. In a circle, or congruent circles, congruent chords have congruent arcs.

Given, AB = 3 and DE = 3.

In the given circle, AB = DE and AB||DE. Hence, AB and DE are congruent chords of the circle.

And In a circle, or congruent circles, congruent chords have congruent arcs.

$

\because {\text{AB}} \cong {\text{DE}} \\

\therefore {\text{arc(AB) = arc(DE)}} \\

\Rightarrow {\text{ z = }}{90^ \circ } \\

$

Hence, the required answer is z = ${90^ \circ }$

Note:- In these types of questions, the key concept is the theorems of circles and chords. In a circle, or congruent circles, congruent chords have congruent arcs.

Last updated date: 19th Sep 2023

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