unit exam - circles

find the value of x.

x = ?

Question

unit exam - circles

find the value of x.

x = ?

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Congruent Chords Theorem", "Equidistant Chords Theorem" ], "new_concepts": [], "current_concepts": [ "Congruent Chords Theorem", "Equidistant Chords Theorem" ] } ## Identify the geometric relationship $$ \begin{aligned} &\text{Chord}_1 = 22 \ &\text{Chord}_2 = 22 \ &\text{Chord}_1 = \text{Chord}_2 \implies \text{Chords are congruent} \end{aligned} $$ ## Apply the Equidistant Chords Theorem $$ \begin{aligned} &d(\text{Center}, \text{Chord}_1) = d(\text{Center}, \text{Chord}_2) \ &x = 6 \end{aligned} $$ Find the value of x. $x =$ 6 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Equidistant Chords Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the geometric relationship

Apply the Equidistant Chords Theorem

Answer: