question 9 of 10

what is the length of chord $\overline{cd}$ in $\odot o$ below?

a. 10 units
b. 2.5 units
c. 5.70 units
d. 5 units

Question

question 9 of 10

what is the length of chord $\overline{cd}$ in $\odot o$ below?

a. 10 units
b. 2.5 units
c. 5.70 units
d. 5 units

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Equidistant Chords Theorem", "Chord Definition" ], "new_concepts": [], "current_concepts": [ "Equidistant Chords Theorem", "Chord Definition", "Circle Theorems" ] } ## Identify the given values and geometric relationships $$ \begin{aligned} &\text{Distance from center } O \text{ to chord } AB = 5.70\ &\text{Distance from center } O \text{ to chord } CD = 5.70\ &AB = 5 \end{aligned} $$ ## Apply the Equidistant Chords Theorem $$ \begin{aligned} &\text{Since the distances from the center } O \text{ to both chords are equal (5.70), the chords are congruent:}\ &CD = AB = 5 \end{aligned} $$

A. 10 units

B. 2.5 units

C. 5.70 units

D. 5 units

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Equidistant Chords Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given values and geometric relationships

Apply the Equidistant Chords Theorem

Answer: