circle a has two chords that are equidistant from the center. if $de = 6$, what is the length of $cb$?

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Equidistant Chords Theorem" ], "current_concepts": [ "Equidistant Chords Theorem", "Circle Geometry" ] } ## State the Equidistant Chords Theorem $$ \text{If two chords in a circle are equidistant from the center, then they are congruent in length.} $$ ## Apply the theorem to the given circle $$ \begin{aligned} &d(A, CB) = d(A, DE) \implies CB \cong DE \ &CB = DE \end{aligned} $$ ## Calculate the length of CB $$ \begin{aligned} &DE = 6 \ &CB = 6 \end{aligned} $$ 6 { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Equidistant Chords Theorem" ] }

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Question

Explanation:

State the Equidistant Chords Theorem

Apply the theorem to the given circle

Calculate the length of CB

Answer: