if the blue radius below is perpendicular to the green chord and the segment $\overline{ab}$ is 6 units long, what is the length of the chord?

a. 12 units
b. 3 units
c. 6 units
d. 18 units

Question

if the blue radius below is perpendicular to the green chord and the segment $\overline{ab}$ is 6 units long, what is the length of the chord?

a. 12 units
b. 3 units
c. 6 units
d. 18 units

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Perpendicular Bisector of a Chord" ], "new_concepts": [], "current_concepts": [ "Perpendicular Bisector of a Chord", "Chord Definition", "Circle Theorems" ] } ## Identify the geometric relationship $$ \begin{aligned} &\text{Radius } OD \perp \text{ Chord } AC \text{ at point } B \ &AB = BC \end{aligned} $$ ## Calculate the length of the chord $$ \begin{aligned} &AB = 6 \ &AC = AB + BC = 6 + 6 = 12 \end{aligned} $$

A. 12 units

B. 3 units

C. 6 units

D. 18 units

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Perpendicular Bisector of a Chord" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the geometric relationship

Calculate the length of the chord

Answer: