Question

assume that two chords in a given circle are congruent. which of the following must also be true?

a. they must be perpendicular.
b. they must be diameters of the circle.
c. they must form an angle.
d. they must be equidistant from the center of the circle.

Explanation:

Analyze the properties of congruent chords

$$ \text{Chord } AB \cong \text{Chord } CD $$

Apply the Equidistant Chords Theorem

$$ d(O, AB) = d(O, CD) $$

Evaluate the given options

$$ \text{Option D is the direct statement of the Equidistant Chords Theorem.} $$

Answer:

• A. They must be perpendicular.
• B. They must be diameters of the circle.
• C. They must form an angle.
• D. They must be equidistant from the center of the circle. (Correct answer)