Question

In the figure, if AB ≅ CD, then

A. AB ⊥ CD
B. CE ≅ BE
C. ∠CEA ≅ ∠CEB.
D. arc AB ≅ arc CD.

Answer 1

D. arc AB ≅ arc CD ...................

Answer 2

Answer:

D. arc AB ≅ arc CD.

Step-by-step explanation:

To solve this problem, we need to use the Intersecting Chords Theorem which states "when two chords intersect each other inside a circle, the products of their segments are equal".

Applying this theorem, we have

$AE \times EB = CE \times ED$

Where $AB=AE+EB$ and $CD=CE+ED$, also $AB \cong CD$, which means

$AE+EB=CE+ED$

However, if both chords are equal, then their arcs are also equal, that's the easiest way to deduct it, that is

$arc(AB) \cong arc(CD)$

Because an arc is defined by its chord basically, and in this case they are congruent.