chords and arcs
find the value of x.
(x = ?)

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Equidistant Chords Theorem", "Perpendicular Bisector of Chord" ], "new_concepts": [], "current_concepts": [ "Equidistant Chords Theorem", "Perpendicular Bisector of Chord" ] } ## Identify the given geometric properties Using the **Perpendicular Bisector of Chord** knowledge point $$ \begin{aligned} &\text{The perpendicular segments from the center bisect each chord.}\ &\text{The given half-chord lengths are both } 12. \end{aligned} $$ ## Apply the chord congruence relation Using the **Equidistant Chords Theorem** knowledge point $$ \begin{aligned} &\text{Since both chords are bisected into segments of length } 12,\ &\text{the total length of each chord is } 2 \times 12 = 24.\ &\text{Congruent chords are equidistant from the center of the circle.} \end{aligned} $$ ## Solve for the unknown distance x Using the **Equidistant Chords Theorem** knowledge point $$ \begin{aligned} &x = 10 \end{aligned} $$ Find the value of x. $x =$ 10 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Equidistant Chords Theorem" ] }

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Question

Explanation:

Identify the given geometric properties

Apply the chord congruence relation

Solve for the unknown distance x

Answer: