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In the figure, if AB ≅ CD, then

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

In the figure, if AB ≅ CD, then A. AB ⊥ CD B. CE ≅ BE C. ∠CEA ≅ ∠CEB. D. arc AB ≅ arc-example-1

2 Answers

3 votes
D. arc AB ≅ arc CD ...................
User Tinsa
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4 votes

Answer:

D. arc AB ≅ arc CD.

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 * EB = CE * 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.

User Ade Yahya
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7.9k points