if the blue radius below is perpendicular to the chord $\overline{ac}$, which is 14 units long, what is the length of the segment $\overline{ab}$?

a. 3.5 units
b. 14 units
c. 7 units
d. 28 units

Question

if the blue radius below is perpendicular to the chord $\overline{ac}$, which is 14 units long, what is the length of the segment $\overline{ab}$?

a. 3.5 units
b. 14 units
c. 7 units
d. 28 units

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Chord Definition", "Circle Theorems" ], "new_concepts": [ "Perpendicular Bisector of a Chord" ], "current_concepts": [ "Chord Definition", "Circle Theorems", "Perpendicular Bisector of a Chord" ] } ## Identify the given geometric properties $$ \begin{aligned} &AC = 14 \ &OB \perp AC \end{aligned} $$ ## Apply the perpendicular chord theorem $$ \begin{aligned} &AB = BC = \frac{1}{2} AC \end{aligned} $$ ## Calculate the length of segment AB $$ \begin{aligned} &AB = \frac{1}{2} \times 14 = 7 \text{ units} \end{aligned} $$

A. 3.5 units

B. 14 units

C. 7 units

D. 28 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 given geometric properties

Apply the perpendicular chord theorem

Calculate the length of segment AB

Answer: