Question

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

Answer 1

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.