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