true or false? the segment $\overline{ab}$ is congruent to the segment $\overline{bc}$.

a. true
b. false

Question

true or false? the segment $\overline{ab}$ is congruent to the segment $\overline{bc}$.

a. true
b. false

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", "Circle Theorems" ] } ## Identify the geometric components and given relationships $$ \begin{aligned} &\text{Circle with center } O\ &\text{Chord } \overline{AC}\ &\text{Radius/diameter segment passing through } B \text{ perpendicular to } \overline{AC} \end{aligned} $$ ## Apply the perpendicular bisector theorem for chords $$ \begin{aligned} &\text{If a diameter or radius is perpendicular to a chord, then it bisects the chord.}\ &\overline{OB} \perp \overline{AC} \implies AB = BC \end{aligned} $$ ## Determine the truth value of the statement $$ \begin{aligned} &AB = BC \implies \overline{AB} \cong \overline{BC}\ &\text{Statement is True.} \end{aligned} $$

A. True

B. False

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

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Question

Explanation:

Identify the geometric components and given relationships

Apply the perpendicular bisector theorem for chords

Determine the truth value of the statement

Answer: