consider the diagram.
what is the length of segment ab?
7
9
18
25

Question

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 Theorem" ], "new_concepts": [], "current_concepts": [ "Perpendicular Bisector Theorem", "Congruent Segments" ] } ## Identify the geometric properties of line l $$ \begin{aligned} &l \perp AC \ &AB = BC \ &\text{Therefore, line } l \text{ is the perpendicular bisector of segment } AC. \end{aligned} $$ ## Apply the Perpendicular Bisector Theorem $$ \begin{aligned} &D \text{ lies on line } l \ &AD = CD = 16 \end{aligned} $$ ## Calculate the length of segment AB $$ \begin{aligned} &BC = 9 \ &AB = BC = 9 \end{aligned} $$

(A) 7

(B) 9

(C) 18

(D) 25

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

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QUESTION IMAGE

Question

Explanation:

Identify the geometric properties of line l

Apply the Perpendicular Bisector Theorem

Calculate the length of segment AB

Answer: